OK, I'm not too experienced, but maybe this might help anyway.
So, if I've read & understand this all correctly, you guys aren't what one would call friends or so, but you know each other, you're introduced to one another. By the way, she was asking questions: who exactly? All of you guys? Or was she targeting you specifically? In the latter case, that's NICE: she's already quite interested in you. The former doesn't really say much, so I'd say you definitely should try to get a 1-on-1-conversation with her asap.
Or a 1-on-2-conversation, where the 2 is: she and a girl friend of hers. That's a situation I find myself most relaxed in: you get to talk to both of them, so anxiety/nervousness tends to have less of a chance. Actually, you probably won't be nervous towards the friend at all, since you're not interested in her (yet!). That means at least part of your conversation will be fully relaxed. Plus, if the friend thinks you're cool, the girl of your interest has a higher chance of starting to think this as well.
Anyway, go up to the girl! Keep in mind: you'll lose her forever if you don't. OK, that's overly dramatic, but maybe it helps to keep you motivated. If she's busy yet again, maybe use a line of banter (oh my, I am not good at this, but maybe I'd say something like "hey, you're the dancer, aren't you? So, is this, like, your dancing crew?"). But please make up something you feel comfortable with, since you'll feel awkward repeating something someone else said, and you'll be much more relaxed when you say something that comes straight from the soul. Make and keep solid and confident eye contact. I find that helps me most to have a relaxed conversation with a pretty girl.
Then, I'd try to 'isolate' her, so I'd be able to have a conversation with her and with her only (OK, and maybe the friend I mentioned above), without 'friends' interrupting (or even other guys - brrrr). I'd ask her some things about how she's doing right now at school - or about her hobbies, if you know of any of them, since people generally do not like to talk about school or work that much. Maybe ask her what she'd like to do when she finishes school, ask her about what interests her, ask her about something emotional. Oh, and I always try to get the girl to laugh, and to have a bit of tension in our conversation (flirty eye contact, etc).
Oh yes, touch her. Just on the arm (I always go for the elbow, because that's a spot nobody will consciously notice you touching it, but will help build a connection - psychologically 'proven'). Don't touch for too long, just for a sec or so. Do it from the beginning. Maybe even to start the conversation (touch - "hey, I saw you dancing the other night, and I wondered what you thought about my salsa moves - you know, the ones that actually looked like cha cha cha?").
This helped me get facebook friendships, some phone numbers, and even a date. Most of all, it helped me to get more and more of a kick out of interacting with women.
So take what I've said with the necessary grains of salt. But: go for it! You'll feel good afterwards, no matter what the outcome will be.
