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Ask to walk with her to class? Or ask her to help you study for an exam in the library. If you've built up comfort getting one and one time shouldn't be that difficult. It will help the conversation be more personal.
So you can't go up and just say hi? Approaching in a group is the best way to build a relationship as people are more relaxed. Win her friends over so they don't shoot you down then talk to her. You must have some breaks where you see here.
I used to be like that but I talked to alot of girls and they rarely flat out reject you. They do it very gently if at all. Just don't be over poweringly nice or a twat and you should get on great.