I've started getting into trying to talk to women more - improve myself socially, and so forth. My college has a cafeteria system where a lot of people eat, but I noticed nobody ever really talks to anyone so I made it my goal to pick out a girl at each meal, sit beside her and just try to open up conversation with her while practicing stuff like strong body language and possibly conversational topics.

Now the first girl I tried to do this with was fairly successful. Chatted for the better part of an hour, had reciprocal interests as me and I was able to maintain her attention even after the interruption of the cafeteria closing/cleaning staff. I normally tend to let conversations drift with bad body language and a lack of interest so it was pretty substantial for me.

Unfortunately, I made the mistake of not trying to get her number as I wasn't sure how well it would be received (I'm 24, she would be around 19 and a topic that came up was that she was friends with one of my co-workers/friends/fellow students). Also I still have a tendency to revert to passive instincts when surprised, which I'm working on (ie I'm a coward and need time to psych myself up to do things). Since then after polling friends on the issue of graduate students dating undergraduates, I came to the conclusion that it was actually generally OK and not super creepy.

Now my question is, is it even possible to ask her out if I talk with her again, or should I forget about it? I have been continuing to practice with other girls in the meantime but she was really hot and I was substantially more attracted to her than most girls I see. If it is possible, obviously I can't just approach it like I don't know her at all but I'm not sure what to do.

I'm fine with rejection but I have difficulty with tunnel vision until I get that rejection :(