I had that problem too. I had difficulty initiating casual contact with girls/women, which was anything between with a macho-like high-five and full-on making out, not including the "endpoints". What really helped me in that department is taking dance classes. Partner dancing is all about casual contact, with most dances being done in either double handhold or closed position. So when I started taking dance classes, frequent casual contact was somewhat of a big deal, especially considering that as an aspie guy, very few women showed enough romantic interest in me to allow anything more than an A-frame hug (shoulders touching, hips at least a foot apart). But over the years, it's become something that was just another part of dancing, not a big deal by any means. I just accepted it as something that happens when you dance with a partner, rather than something I have to worry about.
Having been taking dance classes for quite some time, I managed to get good at it, and the skills I picked up in specific dances (ballroom, Latin, etc.) carried over to freestyle dancing in clubs. And being a good dancer does wonders in acquiring romantic interest. I noticed that when you're a good dancer, you can get away with quite a bit of near-sexual contact, such as momentarily pressing your partner against you and making it look like just another part of a dance move you're doing.