Work on sitting trot first, that way when you are actually in the downward transition, you’re ready for the bounciness! Just keep working on your transitions and in time, you’ll get used to it. You can’t make your horse not bouncy, so you just have to adapt and do your best.
I ride a bumpy horse too! The main thing I do is alot of transition work so you can get him/her really responsive. Another thing I do sometimes is sort of stand up in my stirrups in transitions as it prevents me from bouncing and keeps my weight off the horse's back. Hope this helped you! I know the feeling!
Collect the horse before doing the transition. Also try sitting trot. When your in sitting trot, your could practice not bouncing. Sit deep into saddle and lock your hips bones in. Put you weight down to your heels and imagine you had weights at your ankle. I hope this helped!! :)