If your butt is bruised, imagine how the horse's back feels! When sitting the trot you should not be bouncing or 'hitting the saddle' at all. You should stay in the saddle the entire time, moving with the horse's step. I know, it's easier said than done. Here are some tips:
Relax your hips, sit back and swing your hips with the motion. If done correctly you should be able to feel when each of the horse's front legs comes forwards. Also keep your back nice and supple. Instead of bouncing, absorb the motion by lengthening and shortening the small of your back (in other words, slouching slightly and then straightening your back with every bounce). Be careful not to overdo this. You should only be doing it as much as necessary to stay in sync with the horse. If done correctly, from a viewers standpoint this would look completely natural and smooth.
Good luck, hope that was helpful.