uh....how do you know she's shy? From leaving class on time?
If anything, you'd be the shy one since you're asking how to start a conversation with her, no?
but anyhoo, sit next to her. Then start a convo.
- If you think you can't start a conversation and sound natural, do it by commenting on something visual somewhere in the room. (These desks are tiny. That blackboard is screechy. This class's chairs are comfy. It's so hot in here, is the AC broken? It doesn't really matter what.)
- Or better, comment on something the professor said. Professors always say something worth laughing at or talking about.
- Ask her about the HW even though you know what the HW is.
- Same, ask her when X assignment is due, even though you already have it marked in your planner.
- From there, Ask about her Major/what year/what dorm/etc (not all of these. Choose one. Don't pepper strangers lol)
If she's even the least bit interested she'll ask the same questions back. Go from there.
It's not too hard.