How can you become friends with a girl who is REALLY nervous around you?

Every time you run into her ask her something even if its just one question like how are you> what you do during the weekend and so on so you are getting to know her and getting used to talking to her and vice versa. Just act like yourself don't try to hard, as she can probably pick up on that vibe - she' probably just intimidated cause she doesn't know you that well and likes you so doesn't know how to act or what to say to you. Other than that continue what you have been doing smile, friendliness and persistence. Good luck!