Whoa there, cowboy...
I wouldn't jump right into "Do you want to be in a relationship?" That's a big step. Definitely try hanging out first, ask her out for coffee, bowling, something like that first. Not a movie, not enough chance for conversation there. Somewhere casual. The second or third time you hang out, smile and ask "So can we consider this a date?" If she says no, you can say you were just joking. Less awkwardness for the future then. If she says yes, great! You're now "casually dating". Leave it at that for awhile to feel out the chemistry, then if everything seems right you can ask her if you can call her your girlfriend.
I read somewhere that Aspies like to try to get into relationships right away but don't always understand the baby steps it takes to get there. Unfortunately that doesn't work well, including with other Aspies. So take it slow! Of course, if she tells you she wants to get married tomorrow and have your babies, well, my advice is null and void.
Good luck to you, my friend. Hope everything works out for the best.