you have to relax or else your just bounce out of that saddle like a tennis ball! Singing is a great tip if teddy bears picnic don't work try a spoon full of sugar
Not helpful at all, but when i was 6ish my riding instruct wrote a million pound cheque(ovb not a real one) and put in on the saddleseat, we had to stick our bums down to stop it from flying away. Lol
Not only bareback but two of us up on a Welsh Sec A pony that we sneaked oats to at night and turned him into the devil himself!
If you are bouncing a lot first thing to do is to go sit on a swing and feel what muscles you are using in your backside to push the swing forward - same when on the horse.
Secondly, learn to do a good sitting trot!
If you are bouncing at either the trot or canter, take the reins in one hand and put two fingers under the front of the saddle and 'pull' the saddle off the horses back. This helps you to sit deeper.
Get rid of your stirrups and pray for a soft landing
You can't force yourself not to bounce because you'll tense up and bounce regardless!!
When my instructor was punishing us, I mean, teaching us to sit trot she took away our stirrups and made us all repeat "I-can-feel-the-ry-thm" in time with the beat of the trot. Distracted us from the pain, I mean, focusing on forcing ourselves to sit and once we were all thoroughly distracted and mumbling to ourselves she called canter and naturally all her school horses obeyed her voice command!!!
Such a shame she is not teaching anymore, best instructor I ever had