Side sleeper in bed as well. When I first started hammock camping, I realized side sleeping wasn't very comfortable for me in a simple, gathered end hammock. I couldn't get comfortable until the second night of a camping trip.

Then I suffered a back injury. I could not sleep at all in my bed, so I hung a hammock in my office. I learned to sleep on my back, and after about three months of sleeping in that hammock, my back finally healed. Since that back injury, sleeping on my back in a hammock is easy. Before I go on a camping trip, I usually spend a couple of nights in my office hammock just to get re-acclimated.

Other side sleepers sometimes decide they can't change their sleep habits, so they end up going with bridge hammocks or similar. Personally, I find it easier to change my behavior than throw money at the problem. It might take a while, but I think you can change the way you sleep.