Moderator reminder:
I have already had to go through and clean out this post multiple times. Do not post comments that rely totally on personal experiences. Also do not post conversations about modern cultural bathing practices, including the differences in average weekly bathing sessions between countries.
This question is about the development of high-frequency bathing, please limit responses to that topic.
To better answer your question, there needs to be a distinction between the term "showering" and "bathing". Bathing rituals have come a long way since 19th century America, and methods of cleaning oneself evolved as technologies, like indoor plumbing, become more widespread. The concept of cleanliness in staving off disease also becomes more prevalent with the outbreak of Small Pox and Yellow fever at the turn of the century.
Consider a mid 19th century farmhouse. The main source of water came from a well or spicket outside of the home. Pitchers and basins would be filled with water and people would wash parts of their bodies (primarily their hands and face) while standing. If a home had a bathtub it would be filled in the same way, perhaps some water would be heated first over a fire, and family members would share the bath water. Because bathing was a domestic activity, the responsibility of the family's cleanliness fell to the mother/woman of the household.
Behavioral conduct or etiquette literature, like The American Woman's Home (1869) was written for a female audience and instructed them on how to maintain a socially acceptable Christian home. According to this primary source, the authors refute the idea of immersing your whole body in a bath, stating that "a wet towel , applied every morning to the skin, followed by friction in pure air, is all that is absolutely needed" (Beecher and Stowe, 156). The use of warm water is also not as popular as cool baths, because of scientific postulations that cool water helps in reducing fevers and thus is more beneficial to one's overall health. Keep in mind that this is only one view of the era and indoor plumbing was making its way into more homes.
In Kathleen Brown's work, Society and the Sexes in the Modern World : Foul Bodies : Cleanliness and the Making of the Modern Body, she suggests that the concept of cleanliness, conjured up by the white middle class, was directly associated to one's virtue and subsequently their position within society, which created two general factions, "the diseased and morally dissolute and the healthy and morally wholesome." (Brown 363) However, during the mid-19th century there is still some contention about whether submerging your entire body was wise. Brown notes a 1825 University of Pennsylvania physician, William Dewees, and how his medical advice on bathing "resonates with people willing to wash their bodies while they stood in a basin but unwilling to immerse themselves fully." (Brown 211)
Another book that discusses cleanliness as a civilizing tool is Sickness and Health in America: Readings in the History of Medicine and Public Health. It follows the ideology that cleanliness is an indicator of one's moral capacity. Evidence of this is the "first successful indoor public bathhouse" (487), which opened in New York in 1891, and displayed the phrase "Cleanliness is Next to Godliness" (488) at its entrance. Dirt and odor were synonymous with immorality. To be an outstanding citizen one must show their virtuous superiority by staying clean.
To address your specific concern with showers, here is a very brief history on the shower's emerging popularity in the home. With the growing concern with cleanliness and health at the turn of the 20th century and the coinciding advancement in technology, one could argue that bathing (or showering) became more routine by the 1920's.
Beecher, Catharine Esther, and Harriet Beecher Stowe. The American Woman's Home: Or, Principles of Domestic Science; Being a Guide to the Formation and Maintenance of Economical, Healthful, Beautiful, and Christian Homes. New York: J.B. Ford and;, 1869. Print.
Brown, Kathleen M.. Society and the Sexes in the Modern World : Foul Bodies : Cleanliness and the Making of the Modern Body. New Haven, CT, USA: Yale University Press, 2009. ProQuest ebrary. Web. 21 February 2015.
Leavitt, Judith Walzer, and Ronald L. Numbers, eds. Sickness and Health in America: Readings in the History of Medicine and Public Health. Madison: U of Wisconsin, 1997. Print.
Edit: To answer /u/ctindel 's inquiry about the phrase "cleanliness is next to godliness", it is first mentioned in a sermon of Reverend John Wesley at the end of the 18th century. Most sources that I have found state that a direct quote cannot be linked to the bible, yet the concept itself predates Wesley.
Edit: So glad to be gilded for something I genuinely enjoy doing. Thanks.
As far as eastern regions go, Indians had daily bathing rituals modified to their social strata and class. Evidence can be seen right from the earliest scriptures (from around 1500 BC - Rk Veda - one of the oldest religious texts in the world, the Brihadaranyaka, the Manu Smriti, and the Dharmashastras). Mythology as well, with it being transparently clear by the time of the Ramayana and the mahabharata (both epics, called "histories" in a sense) that bathing was a daily act.
Now this was perhaps because ritual purity is an emblematic aspect of Hinduism. Religion infuses every aspect of life, and therefore being ritually pure was a necessity that could not be avoided : the upper strata needed to be 'pure' in order to establish dominance and legitimate their hegemonic control of both the masses and other ceremonial control of rituals (the latter leads to the former), and the lower strata had to be ritually 'pure' because they would not get to serve the upper class (and therefore not be able to survive, due to lack of work, constrained resources, and social castigation).
There is also some evidence of bathing and general cleanliness leading to higher success in avoiding diseases and death.
Source: some parts from Hindu Ethics: Purity, Abortion, and Euthanasia By Harold G. Coward.
The modern (relatively stringent) social expectations for cleanliness are in large part driven by the kind of mass advertising that got its start around the turn of the 20th century (books describing such here and here ). This was further spurred on by the Social Hygiene Movement among the many Progressivist programs around the 1920's. The Social Hygiene Movement was primarily an effort to curb the rampant spread of venereal disease in a rapidly urbanizing America, and though it was medically off-base in that respect, these two forces continue to influence our modern notions of cleanliness today.
In what society? Upper- class Americans? Middle-class Spaniards? Working-class Italians?
Although this example doesn't reflect upon global tendencies, which would also be difficult to put all under the same hat, it does expand upon how marketing contributed to the every-day-shower standard within a specific cultural context that went through a major transition in the recent history.
A Yugoslavian (or Serbian if you will) poet Duško Radović (1922-1984) is remembered saying
Subota je dan kada se kupaju muževi koji vole svoje žene.
or in English, "Saturday is the bathing day for husbands who love their wives", reminding us that even in modern day history of the 2nd half of 20th century it was not uncommon for people to only bathe once a week. This practice is heavily dependent on the regional cultural context of an average Yugoslavian man's everyday life: work from 6am to 2pm, go home, take a nap, and spend the evening having dinner, watching tv and being around the house. In socialist Yugoslavia it was not that common to be very outgoing, so you would usually spend your week working either in a factory or in an office and be home for the remaining time, so there was also no necessity to smell like morning dew all the time. At the same time, a socialist country such as Yugoslavia praised work and collective work ethics above anything else.
Radović's quote also implies something other than that one should be a clean husband for his wife, and that is that if you were to bathe more than once a week, you were obviously someone who had evening plans, and thus not to be trusted. It was a wide understanding that a faithful and decent, moral man would spend his evenings home, because other options mainly included going to taverns (there were theaters and and cinemas of course, but there was a huge gap in cultural education between the cultural elite and an average working man).
Youth started going out increasingly after Tito died (1980), which was coincidentally just around the time when New Wave music started blooming in Yugoslavia (1979). A personified moral standard gone, with a new culture fighting it's way through, resulted in youth enjoying life to the fullest, so everyday going out quickly became a standard. This seems a little too obvious, but with more outgoing came more mingling and flirting, for which you obviously wanted to also smell good.
The generational conflict of values in Yugoslavia from 1980 and onward is observed with unusual intensity. While U.S.A. has of course seen the grumpy old dad not understanding the ways of "today's kids", the Yugoslavian grumpy old dad in comparison soon had no moral or work standard to hold on to any more - a civil war broke in 1989 and a once country was shattered to barely functional state units with shaky economies, leaving many unemployed and even more disappointed that what they used to live by was now left in the mud to be further destroyed by boots of nationalism. The youth was now 10 years older, mainly not caring about either nationalism or the old socialist ways, and the youth that came after them continued going out more and more.
When the last socialistic regime in the region, that of Slobodan Milošević in Serbia fell, within a year everyone started looking for new models of everyday life and many (secretly) turned to the youth as they were mostly unaware of the old ways. Middle age crisis spread like a disease and metrosexuals were everywhere. More new hair and body products came from the west.
So since 1989 and the Europe-wide fall of communist and socialist regimes is de facto responsible for the spreading of liberal market and intense media marketing that came from capitalistic countries, the fall of Berlin Wall really is responsible for people showering more often in the recent history of eastern Europe.
Too add to this, how come people did not really understand hygiene? surely having clean hands and skin was much preferable to being dirty all the time?
The modern shower requires a domestic heated water supply. In New Zealand that was starting to become widely available in the 1950s. 1951: "No modern home is complete without an efficient hot water service. In this respect most New Zealand homes are by world standards particularly well equipped with hot water on tap to kitchen sink, laundry, bath and wash hand basin — some include a hot shower. The problem is to provide a really satisfactory flow of hot water for all these purposes as often as it is needed. "
In 1971, in households that had hot water, 59% mainly or solely used the bath. 25% used the shower.
By 2005 that changed to 94% using, or mainly using, shower.
Source: Household Energy End-Use Project - Hot water page 255.
Extra Question: How long would I have to not shower for before my hygiene effected my health? In the 1500s? In the 1800s? and 25 years ago?
Lucy Worsley's fun documentary about homes in the house and their evolution sheds some light on this. Most of the videos have been taken down on YouTube, so here's a private copy I use occasionally.
NOTE: I am offering this in the spirit of Fair Use rights (for educational purposes to a limited audience for a limited time) but this video might still be taken down by YouTube whilst they review appropriate copyright law on the video.