I'm not exactly sure what sort of dancing you mean, but you mention it twice and I happen to have some background in dancing in a variety of styles. And since you seem to be somewhere in the SF Bay Area, I strongly recommend the social dancing lessons taught by Richard Powers at Stanford and in Palo Alto as a venue to learn/practice both social and dancing skills. I found it to be an extremely welcoming community and low-pressure environment to learn. Friday Night Waltz which occurs in both Palo Alto and East Bay is also a great community.

"Social dance" is similar in content to ballroom dancing, but recreational and more improvisational in approach. Skill will let you dance comfortably and enjoyably with someone you've just met. I think this style of dancing helps a lot with the social ability stuff too, because you learn how to send and interpret body language signals, and you have to interact on a basic social level with lots of people in a short period of time. There's a rather explicit expectation that asking someone to dance is not a romantic overture, which I (and many others) find comforting.

Of course, YMMV on any/all of this.