If you like her and think that she likes you then go for it, you don't want to be wondering "what if" for the rest of your life, if she freaks when you tell her you're trans then at least you know that she was never worth it, if you say nothing then you'll never know what might have happened if she doesn't pluck up the courage to talk to you first.
It doesn't sound like you're the type of guy who would, but I would really recommend not getting into a relationship, or something not quite a relationship but more than a friendship, and telling her that you're trans after. Me not telling my girlfriend that I was trans for almost a year (my situation is/was different to yours though, I'm still living under female labels) was potentially more painful to her than the fact that I wasn't the lesbian she thought I was. I was lucky that she could see how hard it would have been to come out, and how terrified I was when she asked to speak to me about it, but I don't suppose everyone is that tolerant.
Honesty is the best policy, when you're somewhere quiet together, just bring up the time she saw your birthname and say something like, "You know when I looked up my code for the cafeteria and my old name was on there? I don't know whether you've worked it out but I'm trans and I trust you enough to tell you." Then I'd wait a little while to see how that sinks in if she doesn't say that she knew already, and then ask her out, but that's how I'd try and do it. Of course I'd balls it all up and do the complete opposite ha.
