I'd just say no thanks, that I am too busy getting ready to move.
You're anti-social? I wouldn't have guessed that. I think you just don't like these people! When I moved back to MA, I invited many people over for dinner or dessert, just as I always did in AZ. Every single invitation was rebuffed. I don't know, this was normal to me. If I didn't like the people after one "date," then that was it. We've always been more involved with friends than with family (except our kids, of course) and that just isn't the case for a lot of people.
Well, I digress. You'll be able to meet lots of people you have stuff in common with, once you move.