Will pursuing her make me look desperate?

It would be hard to change her mind by just calling her. You have to meet up with her or something. Or by chance bump into her somewhere.

Ummm I really don't think so either she liked you or she didn't well if you go to that same bar and she gives you her number again then maybe....

Nope - I don't think there is a way. Girls either like you right away or they don't (this is true even when friends turn into lovers - just takes longer for her to open up). If you get shot down the first time, the best thing to do is move on.

Worst thing that can happen is she likes you enough to pay some attention and you fall for her harder. Now you desperately want a girl who doesn't see you as a potential partner. You don't need that.