1) You ARE a biker chick. Just 'cause some other bikers have hangups it doesn't change the fact that you RIDE, really ride.
2) If you can find a club that's dedicated to people of all abilities join their rides (in some clubs you don't have to be a member) and see how you feel. Don't be suprised if you pass people, either. Find a well supported ride. Your LBS might be able to help you find one. I never thought I was all that fast mountain biking and was always apologizing for holding up the dudes I rode with but you know, I not only won the first race I was talked into as a beginner, I passed all of the expert women and beat them as well (we have a very small pond). Don't worry about what you can't do-work on what you can and most of all-enjoy doing it.
3) Don't worry about the bike you ride. It'll get you where you want to go just fine and it'll suprise the heck out of strangers when you show you aren't the typical oversized got the bike out of the garage for the first time in months kind of rider-'cause it will show. Don't let someone else's attitude limit you.
4) Wave or nod hello, if you want. Who cares if they don't return it?
I started this wearing tank tops and denim shorts with hiking boots. It took a little while but once people got past the image they realized I could ride ok and I was willing to learn. I no longer wear the afformentioned items (learned the comfort in bike shorts-once I got past the diaper feeling) and I've slowly changed bikes from the very basic to a higher-end version so I can go faster but as I've ridden with others I've learned I can only be who I am and they can either accept that or not. They usually accept once they get to know me. The others-piss on em!
Best of luck meeting your goals and other great riders! I have a feeling you'll do just fine!
I used to have an open mind but my brains kept falling out.