I think the best way to handle it is to suggest something fun that (subtext) you are already doing, involves little commitment, is public/semi public, she can bring her friends to as a safety net. Although a lot of these things go against Aspie nature. it's important she feel safe and not trapped literary or by pre-committing to something.
A good example would be "There's a free concert in the part, me and some friends are coming, you should come."
Here reply might be "Sounds fun, I might check it out"
Note, you didn't directly ask her out, she never committed to anything, you seem like a cool person doing cool things, if she doesn't go you're still a cool person doing cool things, no direct rejection. She can pop in without being caught with someone that makes her uncomfortable (I'm sure you aren't, that's what she's checking).