So I wanna ask out this girl from my university. We take a few of the same classes and I expect this will be the case in the upcoming semesters as well. We have some mutual friends, but have never been introduced. Exchanged a few words here and there over the last couple of weeks. Yesterday we were sitting at the same table in the HW room (a friend of hers was also there), so I figured I'll start a conversation. Talked for like 10-15 minutes, she seemed to respond pretty well.

I don't know for sure if she is single. Could add her on Facebook to see, but tbh I'd rather talk face to face for now. Am I right to wait with FB or should I just add her?

Secondly, I don't really want to ask her out right away. If I did, it wouldn't be that big a deal, and generally I don't like all this beating around the bush stuff, but this is someone I pretty much see daily so I'd rather avoid potential awkwardness. What do you guys think? Should I ask first if she wants to study together one evening or just not give a shit and ask her out?

Thanks.