The key to not bouncing in the saddle is that you actually have to move A LOT. A rider gives the “illusion of stillness” by moving exactly with their horse and absorbing the motion of the horse with their body.
To keep from bouncing, your hips, knees, ankles, lower back, and elbows all must be moving and acting as shock absorbers to take up the motion of the horse. If any one of these areas is frozen or locked, the rider will bounce in the saddle.
A bouncing rider that slaps into the saddle is VERY uncomfortable for the horse as horses have very sensitive backs. It is so important that the rider is fit, symmetrical, and in control of their body!
Hope this helps!
Happy Riding!
Amelia