To pursue or not to pursue, that is the question...

So this entire school year, I've had this huge crush on this girl in my AP World History class. She's really pretty and smart and I've had it pretty bad this whole year. I asked around and heard she was bi, so it is possible that she could be attracted to me. I've also gotten some signs from her that at least indicate some interest in me, I was "randomly" put into her field trip group with her and all her friends, and this is going to sound corny, but we always make eye contact during class for long amounts of time and it feels really intense and makes me feel super connected with her. I'd really like to ask her out, but I have a couple of fears. First, she's the type that's very flirty and sometimes I wonder if she acts the way she does around me with a bunch of other people. Second, I've never really asked out or openly dated girls since before this year I was closeted and dated guys, and I'm really nervous and am not really sure how to approach that. So what do you guys think? Is it worth trying to pursue?