Hi, before I start I want to say that I'm new to this PUA thing and this is my first post. I'm looking for help on a certain situation. Also, I'm not very social and I usually stay to myself most of the time.

NOTE:The school year is ALMOST OVER and I have class with her twice a week (As far as I know)
AND, she's new to the school so I'm probably one of the first people to actually talk to her. Is that bad? could that mean I'm likely to end up in the friend zone?

Okay so I went to school and I saw this new girl in my class. she sat in the back row and I knew she was new to the school because I never seen her before. I sat in the back row also 1 seat spaced between us and I wanted to talk to her but I was nervous. Before class ended I managed to move to the seat next to her, and after a few minutes i asked what time the class ends (Though i already knew). She answered and suddenly we started talking about common things like music interest etc. she also told me it was her 2nd day at the school. I haven't made much eye contact and didn't smile as much but I noticed I had her attention. The bell rung and ended our discussion early and she asked what my next class was. I told her and she told me hers, then we departed. Stupid me I forgot to ask her name.. but I can probably use that as a opener for next time we meet.

I want to get her number and possibly see if we can have something together. The only problems are the following. 1. School is almost over 2. I only get to see her twice a week (tues&thursday) 3.Convos in class can be strange because its usually very QUIET and everyone might hear me talk. 4.shes new and I'm sure lots of dudes will be trying to get at her.
What should I say when we see each other again?
And how do I keep a conversation consistent without asking to many question? PLEASE HELP!
And most important what can I do to talk to her OUTSIDE OF THE CLASS??