My horse has a very bouncy trot and I know exactly how you feel. My traniner and I have been working on my seat and leg position at the sittng trot and it has helped tremendously at shows. Just sit up act like it's no big deal.
I've had these problems as well, and it was even harder to overcome them as I was riding a bouncy horse who was much too small for me. These tips are very helpful though.
Sometimes my horse does the same thing and I tried some of these tips and they seem to work and my horse doesn't feel as bouncy -or maybe I am getting used to it- but I haven't shown yet but my trainer says I look better.
Try the sitting trot without stirrups for a while - it helped me alot when i was trying to learn how to go with my horse. Hope it might help.
Sounds like someone doesn't have their horse collected and the back is hollow. Any horse is easy to sit if their back is up