Can anyone help me meet this introverted girl?

[bassbrotha]

I need some help to start a conversation with this girl.
I am 17, in senior year of highschool and whenever I go to the school library I always see this girl that happens to catch my eye. Normally I have no problem meeting girls, I have enough confidence to introduce myself, but this one I’m interested in is a lot more quiet and introverted than the rest, making it difficult. She is a girl who does not go out to parties and such and chooses to only have a few close friends, so meeting her at a social venue will not work in this case. I’ve sat with her a few times with mutual friends present, but I can’t really get her in the conversation too much because other people just butt in the conversation and start talking to me while she stays to herself. But when I do get responses out of her, we get along great! We exchange smiles whenever I see her, but I’ve never had the chance to meet her one on one, which I’ve been dying for (because she will usually sit with one or two friends in the library)

Also, I have no classes with her, since she wants to go into the arts and I want to be a physicist/ engineer

So I’m not asking how to start a relationship with her, I just want to know how to meet her first, see what she is about. Im confident when it comes to my looks and abillity to carry a conversation, but it seems I can never get her alone and just talk to her one on one. All I need help with is how to formally introduce myself to her once so I can start talking to her without the assistance of others, I will be fine from there.

Thank you very much for any help you guys can attribute. This has been bugging me for a long time, any suggestion is greatly appreachated!

[confused&single]

Sounds like you just need to pull her aside when you see her in the hallway. If she's with her friends, just say "hey, can I talk to you for a sec?" and motion to a more private location. Then just ask her if she'd be interested in going out to dinner or whatever. If she's returning "longing gazes" and smiles chances are you won't get rejected. I am and was more so in high school an introverted girl and would have LOVED for the guy to just come up to me and ask. The whole, she's with her friends thing is honestly just an excuse. You could ask her to speak privately for a minute when she's with other people. Or maybe if you are all at lunch you could say "Hey "insert her name here" I'm craving a soda (or whatever) want to go get one with me?" then that's your excuse to get her by herself for a minute and ask for her number or a date. Just go for it! Trust me...you generally regret the things you didn't do instead of the things you did in situations like this. Hope this is sort of helpful.