I would suggest walking circles before you go into the trot, especially if bareback. Start with a large circle, both directions and then slowly start closing in the circle. While riding the circle, work up from a walk to a "working walk," which is just a faster walk, but not quite a trot. Your muscles will have to really start working at the working walk. You will tighten up in the beginning of this exercise, but ride it out. The tighter your circles become and the longer you ride, the more your muscles WILL begin to loosen up, and it will prepare you to "ease" into a trot a lot easier than your average walk to trot transition.
Also, work on walk/ stop/ back transitions. Walk on for 10 feet or so, then promptly stop, then have your horse back 4 or 5 steps. This will keep your body guessing (not to mention your horse
) as to what will come next. This will work your whole body at once, where the circles will work your whole body, but it tends to make a particular side work more (whichever direction you are riding.)
It sounds like your have a great horse, so I think he will be able to do these excersises just fine, too. Good luck!