This is an exciting question to answer although also embarrassing that the anarchist in my username is spelled incorrectly.

Anyway, the short answer is 'there wasn't really such a thing.' This question implies another (IMO more interesting) question: how did anarchism become a subculture? I'll answer that below, but first, your question.

So, anarchism emerged in the 19th century, but only in the latter half. Early anarchist thinker Pierre-Joseph Proudhon began writing about anarchism before that: his influential-to-anarchists text, 'What is Property' (in which he quipped that property is theft) was published in 1840. It took time for this to influence people - more attention has been paid to Bakunin but he was one of a whole milieu of libertarian socialists influenced by Proudhon.

You could look at Kristin Ross' 'Communal Luxury', which is about the Paris Commune, not an explicitly anarchist revolt per se. But it involved the famous French anarchist Louise Michel and many of Proudhon's followers. You could quote almost any part of this book for info relevant to the question, but I think this is very sweet

The most general formulation of the goals of Communal education can be found in a poster pasted on walls in the fourth arrondissement and signed by Gustave Lefrançais and Arthur Arnould among others. “To teach the child to love and respect others; to inspire in him the love of justice; to teach him as well that his instruction is undertaken in view of the interests of everyone: these are the moral principles on which henceforth communal education will be based.” (Ross, 2015)

The Paris Commune (for those unfamiliar) was a short-lived experiment in popular rule where the working classes of Paris took power after the government fled. It was crushed mercilessly in less than a year. As I say, we can look at Ross' book for evidence of the kind of world that the anarchists she cites describe.

In general though, anarchism really came into its own with the split in the International Workingmen's Association in 1871, more commonly called the 1st International. I won't relitigate the (historiographically very contentious) reasons for the split but suffice to say that anarchism emerged as an independent trajectory in socialist politics following the split. I'd recommend Wolfgang Eckhardt's excellent book on the split which has some important incidental info on how anarchism took root in Spain and Italy. This somewhat answers your question about Bakunin - an exile from his mother Russia for the whole period in which he identified as an anarchist, he lived mostly in Italy and then Switzerland, though he traveled a fair bit.

Before he joined the 1st international he was involved in building a secret society, something of a necessity at a time when in mainland Europe police repression of socialists was near-universal. Mark Leier's 'Bakunin: The Creative Passion" would be a good place to read about this period in his life, and glean what details you may about the internal culture of socialist secret societies. I think this is the most literal answer to your question: the best place to look for a countercuultural anarchism in his life would be in that secret society, which was called the Social Democratic Alliance (confusing, and unrelated to our current definition of the term). Afterwards, my impression from Eckhardt is that he was a relatively isolated figure who corresponded people largely with letters.

By the 1880s anarchists in America at least had their own publications, for example Johann Most's 'Freedom', or 'Mother Earth' which was founded by Goldman. Anarchists around the world including the US attached particular cultural importance to May Day, which is associated with the Haymarket affair. But it's important to understand American anarchism in the 19th century as essentially a part of a broader socialist movement focused on labour. Thus the founding of the Industrial Workers of the World involved the anarchist Lucy Parsons but also the socialist politicians Eugene V Debs and Daniel DeLeon, all with their own ideas about how socialism should look.

I'm not super familiar with the history of anarchism in Europe before 1900 but in most places it happened primarily underground, and was most successful in Italy and Spain. Particularly in Spain, anarchism ended up being the dominant tendency in socialist politics and there were anarchist schools, anarchist community centers, anarchist youth programs, etc etc. This history was partially suppressed by the Franco regime, which brutally crushed anarchism and all other forms of socialism following its victory in the Spanish Civil War. But some anarchists escaped to exile and kept the memory of the period alive, in this respect I'd recommend Martha Ackelsberg's fantastic book, 'Free Women of Spain'. It is full of interviews with women who belonged to the Mujeres Libres (free women), the women's section of the anarchist union, the CNT (in English, the National Worker's Confederation)

Because of its success, Spanish anarchism is probably the place you will find the most interesting answer to your question, albeit not in the time period you asked about. The Spanish anarchists saw themselves as building a whole new social order in line with their political ideas and so they had programs covering virtually every aspect of life. I am going to wrap up by mentioning Murray Bookchin because he comes into play in answering your other question, and he wrote a book on the history of Spanish anarchism that addresses this stuff in depth.

Anyway this is getting long so I'll just say that this would be a much more exciting question to answer about 1900-1945. By and large anarchists in the English speaking world mixed in multi-tendency socialist spaces - I'm having a tough time finding it but there is a scene in the seminal Warren Beatty film 'Reds' where the journalist John Reed, the anarchist Emma Goldman and others are hanging out in a cafe, presumably Sach's. I don't know if anyone has written about Sach's but if someone reading this does, tell me in the comments!

Oh and PS it's a primary source but Orwell's 'Homage to Catalonia' has some in-depth descriptions of a full on anarchist culture where for example tipping has been abolished. That's from the 30s but it's very interesting reading.

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Speaking of primary sources, you could also read Emma Goldman's enormous autobiography 'Living my Life', which covers her involvement in anarchism at the end of the 19th century and can give you a sense of the mixed socialist milieu that she and other NYC anarchists experienced. It is also the source of the famous (paraphrased) 'If I can't dance, it's not my revolution'. The full quote is as follows:

“I did not believe that a Cause which stood for a beautiful ideal, for anarchism, for release and freedom from convention and prejudice, should demand the denial of life and joy. I insisted that our Cause could not expect me to become a nun and that the movement would not be turned into a cloister. If it meant that, I did not want it. "I want freedom, the right to self-expression, everybody's right to beautiful, radiant things." Anarchism meant that to me, and I would live it in spite of the whole world — prisons, persecution, everything. Yes, even in spite of the condemnation of my own closest comrades I would live my beautiful ideal.”

There were certainly aesthetics, social clubs, and relations among the anarchists but being a rather broad movement at the time it became pronounced in a variety of ways. There are far more stories of the bars and clubs the various radicals and revolutionaries assembled, in one entertaining example one coffee house in Vienna called Cafe Central had at one time been visited by Trotsky, Hitler, Stalin, and a variety of now famous individuals. But I'll focus on the German anarchist movement of New York City near the turn of the century. Most quotes are taken from "Beer and Revolution: The German Anarchist Movement in New York City 1880-1914" by Tom Goyens. And should time permit later, will add an additional story of the French anarchist artist cliques and clubs responsible for the neo-impressionist movement.

By the 1880s and 90s Hoboken was majority German immigrant, among other areas throughout the city. And in the densely populated and poverty striken communities political radicalism took hold. While early radicals were mostly of social-democratic, socialist, or later dubbed "Marxist" varieties, by the 1880's, anarchism in New York City had become "cool."

By 1870, German socialism and later anarchism was deeply rooted in Kleindeutschland. Trade unions, workers associations, mutual-aid societies, and a panoply of cultural and educational groups held meetings in the beerhalls and labor halls of the Lower East Side... clusters of such beerhalls, owned or frequented by anarchists or anarchist groups, were found on First, Fourth, Fifth, and Sixth streets, as well as Avenue A and B and First and Second avenues. This was the center of German anarchist activity during the 1880s...

Additional groups opened or frequented more locations in East Harlem or Yorkville (between 75th and 83rd). Outside of Manhattan German anarchists had social spaces in Buschwick, Williamsburg. One popular hang out for events was Liberty Park,

Liberty Park, situated along Cooper Avenue in Ridgewood... was once advertised to readers of Freiheit [a German Anarchist newspaper] as "the largest park in Greater New York for forest excursions, picnics, national festivals, etc." Its spacious dance pavilion, bowling alleys, rowboats, and playground became the setting for numerous German anarchist festivals, picnics, and dancing events.... The most popular games included ninepins or skittles, sharpshooting, target shooting for children, throwing rings, egg in spoon running.

Anarchists also organized "singing societies" with monthly dues to pay for expenses and social space. They organized large concerts by federations of musicians and singers, at times intermingling with other immigrant communities. One event in April of 1890 "featured German vocalists and a Scandinavian choral group, as well as poetry recitations, comical sketches, and a lecture by Johann Most." Most was a famous anarchist of the time committed to a style of "revolutionary" anarchism that was largely unapologetic for its acceptance of violence and militancy towards its ends. Most elsewhere stated to the New York Times, "I believe in the drama as the most effective propaganda."

I use these examples to show how, while becoming its own culture with clubs and music, it manifested itself within a culture of immigrants who were very much their own segmented population from other parts of the country.

Speaking specifically to cultural trends within the Italian-American anarchist communities - Italian migrants involved in labour activism and radical political movements associated with Anarchism over Socialism or Communism in larger percentages than other migrant groups - Marcella Bencivenni writes on the importance of artistic and cultural production to the spread of the anarchist movement. By the turn of the 20th century, media influenced by anarchist ideology was being produced and performed in places ranging from New York City to Barre (Vermont) to Ybor City (Florida) and dozens of other towns and cities across the United States - and even abroad. That is, poems were written and published in newspapers alongside weekly columns featuring a (fictional) conversation between an anarchist and a member of the peasantry, wherein the anarchist explains the ideology using terms and language the average Italian would comprehend, and these columns were next to advertisements for plays written by anarchists meant to express a working-class culture and ideology.

Often these communities revolved around a core group of radical "intelligentsia," who would meet in members-only clubs or cafes to discuss the movement. These clubs would often be open to the public on Sundays - the day specifically chosen to influence people to come discuss radical activism instead of attend church. Beyond that there were organized public festivals, things like picnics and marches, meant to build ties with the community and spread the ideology, but also just to like, have fun, you know? Eat things together, enjoy the day. There'd be public speeches by well-known anarchists like Malatesta or Galleani, speakers who toured internationally spreading the ideology, trying to gain new converts and establish new radical communities. These speakers were well known, these events were very public, and anyone could buy the newspapers which, though written in Italian, openly advocated for the establishment of an anarchist society while also announcing where and when these picnics would occur.

Relative to your question on subculture, these communities sought to establish an alternative to mainstream society. They created their own holidays, celebrated their own heroes, "baptized" their children into anarchism (weird as that sounds)... Yet, on the surface, this culture appears to be pretty much the exact same as the 'dominant' culture, despite advocating for a fundamentally different kind of society and way of living. Which makes a lot of sense in some ways - the goal was to convince as many people as possible to join the movement, or to, in some way, have them get involved in the labour movement. The most effective way to do this is to spread the message in a language people already speak. Compare this to Punk which - and now I'm completely off any sources so please correct me if I'm wrong - seems to speak a different language entirely, because the point isn't really to spark a mass uprising and worker's revolution like what the 20th century anarchist movement wanted to achieve.

I'm going to take the easy way out and say it kind of depends on how one defines a subculture. Certainly these communities had their own artistic and intellectual output, but often it was meant for broad consumption. This was a culture that wanted to be read and understood, and that actively sought to become dominant.

Sources: Marcella Bencivenni Italian Immigrant Radical Culture: The Idealism of the Sovversivi in the United States, 1890-1940

The Lost World of Italian-American Radicalism, specifically Part III on culture.

Davide Turcato, "Italian Anarchism as a Transnational Movement," IRSH 52 (2007), pp. 407-444