Most Helpful Girl
So you can't start a conversation worth poop, but you don't lack confidence. Sorry, in my opinion they go hand in hand.
She sits next to you in class? ask her about the course, how she is finding it, is she finding any part hard (maybe you are too), ask how she found an assignment, how did she find it, can you offer her help, or even ask for it.
You could start the day with a simple "good morning" followed by a small and simple complement such as "love your hair by the way"
The list is endless, you just lack the confidence with girls. Keep it simple and go for it.