Should I Ask Her Out Or Distance Myself? (10 points)?

It seems like she's trying to be an open social erfly. She knows she can get attention from guys so what you should do is the opposite. Don't give her all that attention and when she says hi to you give her a simple hello. Maybe then she will come more often to talk to you. I'm not saying be rude about it but just give her her space and you live your life.