steal her seat, i like that.
Me too:
"That's my seat."
"wanna share?"
OK, seriously, if she's been"giving you the eye" then she'll probably not be opposed to you sitting next to her. She might also be too shy to approach you, if she is indeed interested.
Also, there's always the good ol' "I missed this part of the lecture/I didn't understand this/help me" in order to get to talk to her. If you time that for right before class, you might not even seem
too outright "pls-date-me" for sitting next to her. (From life experience: I haven't had someone do that (I don't think so, anyway) but I had one kid sit next to me in a computer lounge and ask me what time it was- thing is, the time was displayed right on his computer screen. It was pretty funny and I went on about a date and a half with him, so it "worked." Lol.)
Only other thing I can think of is if you have facebook, you could add her (because it's a college networking thing, it's not too weird to get people randomly adding you, though I'm evil and would outright actually ask guys who added me randomly why they did so- it was usually a very easy guess, lol).
BTW- this doesn't sound like "an aspie thing." More like normal dating agony.