Normally you would first get him looked over by a vet to see if he may be hurting, but if he doesn't do it when you ride with a saddle, it probably is not a problem with his health, so first of all, we need to look at you as the rider.
Do you move a lot on his back when he lopes? Do you fly up in the air and slam down on his back with every stride? Do you use the reins to keep your balance? Either of these can frustrate, confuse, unbalance and even hurt your horse, causing him to buck. So, have an instructor watch you, or a friend video you so you can see if you are the problem.
If you are not pulling his mouth to keep your balance and you have a deep seat and are not moving around and annoying him, the other thing it may be is that your horse knows you are more easily bucked off when you are bareback, so he tries to dump you knowing you are not as secure on his back when you ride bareback as you are with a saddle. To fix this, you need to become become the best rider you can be so that he cannot buck you off, even when you are bareback. If you fall off when he bucks, you are training him to buck. If you stay on, you are teaching him he is just wasting his energy.
Another thing is, he may just be "feeling his oats" Try more turnout if possible so he can get his bucks out in the pasture more, and always do some groundwork before mounting up. It not only warms up his physical body, gets rid of some excess energy, but it also gets him prepared mentally.
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