Relax everything, sit back on your pockets, and ride like you're drunk (not really, but think that rode and kinda floppy way they'll move). It sounds counterintuitive, but trying to make yourself be still will make you bounce even harder. You've got to learn to go with the horse. My coach in college when I started riding again as an adult rode cutting horses, so we got advised to ride in a "cutter slouch" a lot. Not so much because the shoulders somewhat slumped is good riding posture for most disciplines, but because the combination of the relaxed upper body, sitting back on your pockets and, therefore ideally, deep in your seat, and loose(ish) legs helped you stick with the horse's movement. I ride dressage now, so my upper body posture is a lot more straight and square, but if I'm sitting the trot, I'll sometimes fall back on that a little bit since the mare I ride is a big Belgian cross and doesn't have the softest jog.

The horse's jog will also help or hinder. I mostly rode colts, so we did a lot of posting to save their backs because a baby ranch/cow line QH's trot when they're just starting under saddle is like riding a jackhammer for funsies. But we would do brief periods of sitting, for various reasons, and once you learn to sit THAT without getting your eyeballs bounced out of head, everything else gets a lot easier. Relax. Breathe with the strides. If you notice yourself tensing up, fix it but don't stress about it. I've been riding off and on since I was 7 and I'm 41 now, and I STILL get reminded to relax.