I'll be honest with you: I'm afraid you're living in a pretty tough time for asexual folks, especially asexual women. While plenty of people found the free love movement liberating and found that it removed restrictions on behavior that had made them unhappy, a woman like you would have likely felt little more than an increased pressure to do something she already wasn't interested in. And that's more than a little alienating, so of course you'd want to find resources to help you understand what's going on!

If you're into history and have access to a good library, you've probably heard of so-called Boston Marriages which were typically homoromantic but non-sexual relationships between women. (AKA gals being pals.) That might make you feel a little less out in left field, though by the 1960s they unfortunately were history. (Not to say those types of relationships stopped existing, but they stopped being something in the public eye.) Also, if you're not homoromantic, the knowledge of Boston marriages may seem completely inapplicable to you. If there's not a lot to find in the library, we can look to other avenues of learning.

Your instinct to stay away from professionals with this information is spot on. They will almost certainly tell you that there's something wrong with you (your hormones are off, it's all in your head, maybe you just haven't found the right man, maybe if you really tried to want to have sex, etc etc) and want to try to fix it. But you clearly know that there's nothing broken and you don't need their input. So, you start to think that with the homophile and Gay Rights movements growing the way they are there's probably a lot of information out there for people who aren't straight, so surely there's something out there for you, too. Let's look at some of the resources available that speak of the LGBT+ community.

In 1948, Alfred Kinsey published a study on sexuality that had a huge impact on the way Americans viewed the topic because he demonstrated that homosexual behavior (whether in the form of being strictly gay or otherwise) wasn't nearly as rare or as "weird" as people thought it was. His scale ranging from strictly heterosexual to strictly homosexual really opened people's eyes to the spectrum of sexuality and helped pave the way for a wider acceptance of queer folks. What he didn't do, however, is account for asexuality on his scale. Those who reported no sexual desire were marked as X and their data wasn't incorporated into his conclusions. So, I guess Kinsey is out.

What else is there? Well.. not a lot, really. The reason his report was so influential was that it was the first of its kind. On with the search. Where else can you look besides the library, unhelpful professionals, and a book that doesn't include you? If you're in or near a big city (or even visit one) you might be able to connect with the local queer community and get some literature from them, but there's almost no chance that it will include you because those groups were created and populated by people who identified as gay (or lesbian). Again, that's not really helpful in your quest.

What if one day, you flipped on the TV and happened to catch Gilligan's Island, though? The main character is written as asexual (though not overtly identified as such since a) the term wasn't applied to humans at that point and b) there didn't tend to be a ton of discussion about the sexuality of TV characters in the 1960s anyway). So here's a character who is plainly not interested in sex, even when a pretty girl is flirting with him. That might resonate with you even though it's not really teaching you or helping you understand anything. Sometimes just seeing that there's someone out there like you helps make you feel less alone and seeing that his friends accept him for who he is might make you feel brave enough to confide in your own friends.

So, let's talk about your friends. When you say they're the 'artsy variety', I'll assume you mean more worldly and open-minded than the straitlaced people you know. Maybe one or two of them are even gay. How can you expect them to respond? It really depends. Your girlfriends are more likely to think they get it if you tell them simply because for the last many hundreds of years, women weren't supposed to acknowledge that they felt sexual desire even when they did. To the girls in your life, there's a pretty good chance it's going to come across as having conservative views on sex or maybe even trying to convince yourself that you're not interested in having sex because of the ideals of purity that were pushed on you when you were young. They'll probably think you think it's a problem, though, and want to make you feel better so you might get unsolicited advice about how "when you find the right one," everything will be different. (Especially if they're engaged or married and have found their 'right one'.)

As for your male friends, it's a pretty good bet that it will seem really out there to them because the society they've grown up in has taught them that getting sex is one of the most important things - if not the most important thing - a young man should do. Not wanting sex is completely outside their experience (unless they happen to be asexual, too, in which case you might find someone to commiserate over the state of the world with). If you've chosen your friends well, they won't make crass comments about 'helping you with that' or anything of the sort, so I hope you've chosen your friends well.

Depending on where, exactly, you live and how educated on political topics your friends are, they may also view your asexuality as part of the wave of "radical refusal" employed by some members of the Women's Liberation movement who viewed abstaining from sex as a political statement against the growing permissiveness of the country's sexual attitudes. (You and I know that abstinence and asexuality are different, but it's a hard thing to explain to people who don't even realize that asexuality is a valid orientation.) That could definitely factor in to how they react when you tell them, depending on whether they support abstinence as a political statement or not.

As I said in the beginning, the late 60s were a really tough time to be asexual. While there's a chance you will connect with others like you in the local queer community, there's also a chance you won't and there's just not really any information I know of that would help you understand your leanings.

But!

If you can hold on for just a couple of years, things will start to change. In 1972, Lisa Orlando will write The Asexual Manifesto which, while it largely frames asexuality as a political statement as mentioned before, also discusses the way sexual attraction is viewed as essential to every person's having a fulfilling life. A year later, this thread will be picked up by Bernard College's Frances Chapman who writes an article called CHOOSE-YOUR-OWN that explicitly puts forth the idea that a you don't have to have a partner for sexual gratification and you don't have to have sexual gratification to be fulfilled. She references a workshop at a convention on the topic of asexuality by Barbara Getz - who could turn out to be that teacher you were looking for.

In the second half of the decade, the first academic paper on asexuality will be published and before the end of the 1970s, another researcher (Michael Storms) will rework Alfred Kinsey's scale to include asexuality. At this point, there will be people and information that can help you understand yourself and how you fit into the world, though you'll still have to work to seek them out because the idea of there being people who don't feel sexual attraction (and aren't 'broken' because of it) won't come onto the mainstream's radar for several more decades.

edited: added missing words, fixed a tense, removed rogue commas, spelled someone's name correctly, thank you to the person who thought this was worthy of gold (am I supposed to say that? I'm not from around here)