How to talk to this Shy Girl?

So I'm Grade 11 and quite popular, never really had a problem with girls or friends, and are well liked with every group from school. But there is this shy...or quiet by nature girl in my Math class that sits in front of me that I find absolutely beautiful, but it almost seems like she doesn't give her self credit for it, she never talks to anyone in the class and only talks to her small group of "girlfriends", I never see her talk to a male, but I see her almost everywhere at lunch since we hang out at the Commons. But like I said, I traverse with many different groups, even the extremely popular hockey guys, and I've caught her eyeing me down. I'm very sincere and want to just strike up a convo and talk to her, get to know her, let her open up to me...but ever since she caught me talking to really popular people, I feel she's intimidated or something and I am actually scared for once...I almost feel if I ask her for help for a question( something to just light the fire for a conversation ) that she won't even give me the time of day. Can anyone throw some advice on what you think she thinks, and maybe help me establish a plan to even talk to her.