What helps me (not particularly with this issues, but as an overall “what I do when I think I can’t”) is to exaggerate whatever I think I should be doing, because likely, when I think I’m exaggerating it, I’m really doing it to the sufficiency that is needed to maintain proper x, y or z.
I had a horse who was absolutely and ridiculously bouncy. I mean, I felt like he was sending me to the moon and back with every stride. I have never in my life ridden a horse with such a gait nor do I ever think I will again!
do you have anyone who can put you on the lunge line? That way, you don’t have to focus so much on getting the proper roundness etc. but you can focus completely on yourself. I would put my students on a school mare I had with an unfortunate canter (kinda like a pogo stick) on the lunge and take away their stirrups. I would also have them drop the reins and wear white gloves, not necessarily for me to see them, but white gloves makes any rider hyper sensitive to the movement and placement of their hands. If you have a pair, throw them on- rigidity through the whole body is effecting your ability to sit, no doubt you have some tension in your upper body as it’s bracing against what your core and lower body are not absorbing.
I try to think, when I sit the trot, that, starting from my calves, pulling up through my thigh, straight up my core to the top of my head, I’m scooping up and lifting them. Every. Stride. Same goes for the canter, I’m picking them up with my leg and core, and holding that impulsion through the contact with my (elastic elbows) and hands.
Also sounds like your horse isn’t accepting of your seat. You want your seat to be inviting, rewarding, and soft. A bouncy horse is a bouncy horse, you’re only going to be able to do so much with the actual conformation and build resulting in how they move, but when you sit, they should soften. It should be like “oh good, my rider is there, I’m ok, I can relax”. When the horse is relaxed through their back and topline, they’re more fluid and swingy and eventually, a round horse with impulsion will become even bouncier. They should not be as jarring, but yes, bouncy.
And remember, the whole, Rome wasn’t built in a day thing. If you can even sit three strides, take it. Next time aim for five. Aim for half the arena, the whole arena, and build from there.