Today I was in the student union looking for a table to study at. I found one where some girl was sitting and asked if I could sit there. She said sure, so I sat down and started studying. About 45 minutes later she asked me if I knew what time it was, and then we got into about a five minute conversation before she had to take off for her final exam. Everything went well, but it just felt like I would have been moving way too quick about asking for her phone number then. I couldn't think of any way to ask without catching her completely off guard. So I ended up missing out on an opportunity because I'll probably never see her again.

What would you guys recommend I do in the future so that I don't look like some loser who asks out every girl he meets, but also so I don't pass up good opportunities either?

Don't sit there for 45 minutes in silence.

I didn't sit down trying to pick her up. I sat down because I needed to get a lot of reading done, and it just happened that a conversation arose as she was getting ready to leave.

5 Mins is MORE than enough time to get a #. Next time don't worry about inconsequential things like that....it wouldn't matter if you had talked to her for another 10 mins.....she already knew whether she'd give you her # or not.....just go for it....you'll be better for it!