No, I do not think you should try and "win her over." She is in a relationship right now and trying to "steal her away" will only lead to pain and disappointment. You should back off unless and until she is single. She needs to decide for herself who she wants to be with. If she truly wants to be with you, SHE will make that decision and leave her boyfriend.

As a lesbian, I can tell you first-hand that going after a girl who is in a relationship with a man is a BAD idea. When I was in high school, I was in a situation similar to yours. There are bi women who will have relationships with you, and by women who will always date men and only want you "on the side." It's important to learn how to tell the difference so that you don't get hurt. As long as this girl has a bf, you know where you stand. She is with someone else. Leave that alone. If she really wants to be with you, then she will
Leave her bf. But that needs to be her decision. You should not coax or pressure her into it.