Is she playing around or genuine?

Ok girls are never so sure of what they want. Also to add she is probably flattered that you like her, girls love attention and that could be part of the reason she's spending time with you. I can't exactly tell you her true intentions of course because I don't know her, but if she's been with the boyfriend for very long most likely shell stay with him in the end. Just take it slow and be good friends first and see where it goes never expect too much.

It sounds like she doesn't want to give up what she has until you're a sure thing. It's a difficult situation, because you don't want to be the main cause of someone else's break-up; she might actually end up blaming your advances if she later decides to return to her previous partner.

Stay positive around her, but don't be the one to suggest the break-up. Eventually, she'll do the math and pick the best guy for her.

It sounds like she may be testing the waters with you to see if you would be interested in her. If she is indeed having problems with her boyfriend, she may be looking your way. However, her boyfriend is still in the picture, and until they officially break up, its going to be hard for you to establish a relationship with this girl. My advice is to continue to keep as close to this girl as you can, and see if she does break up with her current boyfriend. If she does, you can then pursue her. Good luck!