@BurlyDormouse6247,
Be friends, and not just with her. That is, have conversations, spend time together, and genuinely be interested in other people's lives. I understand that social signals can be difficult when you're on the spectrum.
So here are a few topics which might make things easier, at least to start (with her or anyone else):
- Did you get the homework/understand the assignment/get the notes?
- I have no idea what to do around here. Where's a good place to go for fun? (if they ask what you consider fun, tell them, whether it's bowling or rock climbing or a comedy club or whatever)
- Is the ____ any good? (fill in the blank with anything from the day's special in the cafeteria to whether the school has a film series or the like)
- What are you doing over the break?
Making friends with, and talking to, a lot of different people makes it a lot easier to talk to someone who is important to you. When you master the conversations where the stakes aren't so high, it makes it easier to handle the conversations where the stakes really are high.
You can do it. She (and all women) is a human being just like you. She might be bored or lonely. Or maybe busy. But saying hi and those quick little topics won't bother most people (don't bug her if she is obviously studying). They're quick and painless and unobjectionable.