Relax, sink into your seat (without slouching), loosen your hips, and collect your horse. They smaller their step the less bouncier they are, then you can work on gradually extending it
Try bareback and then no stirrups and then try no stirrups and having your arms out that should help that’s what’s i used on mine X
Do some bareback riding if you can, you get a much better feel for the horses movements and heaps of stirrupless work. Most importantly RELAX, you won't go very far if you tense so just relax into the movement :)
try to let your legs just hang if you are doing stirrup less and really relax in your hips and seat as this is an important shock absorber aside from your knees.
Take stirrups away. Do off horse exercises to build core (yoga, pilates etc) strength. I used to practice in the bush holding onto the pommel, let the horse just trot along in a straight line in soft sand and get a feel for it. Start slowly and build up.
I find it easier to sit the trot without stirrups when I'm getting bounced around a bit. You can wrap your leg around them a bit more and work on your seat
Thighs tight against the saddle, don’t depend fully on you calves
Relax everything in your body and maybe ride without stirrups for a few minutes and the gradually for longer each ride. Then with stirrups have long stirrups
Just remember the basics. Eyes up, heels down, shoulders back, and just relax your body.