My horse is very big, and has the tendency to have a rigid back. So he is very difficult to sit on. However I have been working out and seeking to strengthen my core. It is very important that when you ride you use your abdominal muscles which many times we forget about. Hope I help!!!
stand in a half hault or small halfseat to get off their back so your not jaming them in the back
my mare is also really bouncy, i have started to strengthen my seat by doing a full seat on the straight sides of the ring, and then do a half seat on the curved sides. It has slowly been helping bc now i can do a full seat for 1 full lap, it is definitely hard work. there are so many benefits to having a good seat, you can add more leg, and keep their hind end much more engaged!
Ride lots without stirrups and bareback!