Not sure if you do groundwork but maybe his trot just needs to be slowed down on the ground first without tack, then with tack, then it'll transfer into you when you ride him.
But if you have a lunge line and you know how to use it (if not, it's very easy to learn, by watching videos and pretending a friend is your horse and practicing how to unwind it and send them farther out in the circle) [if that confused you, I can try my best to explain it !]
Then teach your horse half halts.. they are little vibrations (or partial soft stopping cues) that let your horse know something is about to happen, like changing from walk to trot, or that they need to slow down their feet.) You can also work with that on the lunge line and when you're walking him, play with the speeds of his walk. Go from a barely moving his feet walk, to a more active walk, to a very big walk, and then back down.
Are you sitting the trot or are you trying to post? Post can be described as when your horse is trotting and you lift up when his body comes up and "sit down" due to gravity pulling you back down. So, standing in your stirrups is how most beginners start to post.
Either way, sitting trot is VERY bouncy especially when you haven't learned to move your hips with your horse. Posting trot tends to be a TON easier.. so don't be discouraged if you find yourself bouncing around on either.. a horse isn't smooth until YOU are! :)
But I recommend trying those few things out. A lunge line would help so much, or even trotting beside him on the ground in lead rope and halter like you are giving a pony ride, and try to get him to match your speed at the trot.
Hope this helps!!
P.S: I am learning my sitting trot atm and I feel VERY out of control when he goes :P