Practice without stirrups, and then put them back on after a while. Also make sure you are not using the reins to balance, this makes the reins (your horses mouth) become the shock absorber. If you have a friend try putting your horse on the lunge and then practice with no reins, or have your reins very loose. I'm not a natural at sitting trot and I always practice at a loose rein trot so I don't upset my horse. Also don't try to make the movement perfect, just sit! That's the best thing I was told. Practice practice practice and eventually it will become second nature. Good luck!
Think about keeping back and belly between two boards and it may seem stiff but the horse actualy appreciates you hitting the saddle in the same spot more than trying not to bounce. Think about lifting your feet out of the stirrups slightly. The more you press down, the more weight you take out of your seat, the worse you will bounce.
Keep your heals down a lean back .
use your heels as a shock absorber and keep your heels deep
Grip your legs as hard as you can
I agree with Riley
Want to add also stick your chest out
Sit up straight with your toes forward and heels down and go with the horses movement rather than try to absorbe the movement.
Don't squeeze your knees!!!!!!!!
Never ever squeeze with your knees.
Squeeze with your calf and thigh. If you want you can try something dressage riders do, grab like The "fat" from the inside of your thighs and pull it out and up infront of your leg.
Also roll your hips under your body but sit up straight
Squeeze your knees, keep your back straight and stay relaxed. Also work without stirrups, it helps a lot!