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

I think you should ask her out because usually when a girl gets quit when you talk about another girl she likes you and when she was with the other guy she have been trying to make you jealous so you would ask her out. But it sounds like she is starting to accept the fact that you don't like her (or at least that is what she thinks) So you can either ask her out now, or wait and blow it with her.