The only way you are going to get this pony to stop bucking is to find the CAUSE or root of the problem. Just trying to find a way to get him to stop the bucking is not going to permanently fix the problem.
You and your trainer need to find out why the pony is bucking. Then you need to get rid of the cause. Now, once the cause is eliminated, you will need to do some retraining. Your pony has most likely gotten into the habit of bucking, and wont stop even when the cause is eliminated; unless he has some retraining.
What i would do in you situation is this: AFTER the cause of his bucking is eliminated, every time he bucks, he needs to have something happen to him that will make him not want to buck anymore. I would ride him in a halter while doing this so as not to develop a hard mouth. So, basicaly what you need to do is, every time you feel him start to buck, take one rein and bring his head around to the side. Then I would have him do a few circles, stand relaxed for a minute, then continue on riding. This may sound tedious, but he must be discouraged from bucking. I hope this helps!! Let me know if you have any questions :)