This is an interesting training issue. Of course, before you address it from a training standpoint, it is important to rule out any physical problems. If this behavior is new, it is possible that the horse may have a sore or injured back and the bucking is a result of pain. A vet or chiropractic exam should rule this out. Once you are confident it is not a physical problem, then we can address the training issue.
This bucking behavior is commonly seen in lazy or balky horses and can be associated with a refusal or reluctance to move forward. Generally, the way this problem develops is that the horse doesn't want to do whatever is asked and by way of protest, he throws a little buck. It is what happens next that creates or resolves the problem. Often, the rider is taken off guard with the buck and gets flustered or frightened and feels compelled to take control and so grabs the reins and asks the horse to stop. In our human mind, we think we need to regain control and regroup and then try it again. But the horse thinks much differently than we do. In his mind, he thinks, "I do not want to do that and if I just throw a little buck, she'll stop me, which is exactly what I want!" So by stopping the horse, you have, in effect, rewarded his behavior and he has gotten success so he will certainly do it again. He does not have the ability of linear reasoning and he does not put two and two together and realize that you will make him do it again. All he knows is the here and now and what happens immediately.
The solution for this behavior problem is to make the horse actually work harder when he throws a buck, and let him stop when he is relaxed and compliant. This will resolve the problem very quickly, since the horse is acting out of laziness. As soon as he realizes that bucking causes him to have to work harder, he'll give it up. However, this requires a great deal of skill and confidence on the part of the rider and is probably something you'd want a trainer to tackle. Depending on how ingrained this behavior is, he may fight before he gives in. An old adage in horse training says that it always gets worse before it gets better. So I am reluctant to tell you to dig in and get after him, because he may buck even harder at first.
As always, by understanding the way a horse thinks, you are better able to resolve problems. At the very least, when you feel the horse get bucky, make him do something harder, even if it is only circling a tight circle at a trot and only let him stop when you feel his back relax. I hope this helps!
_________________________________
If you liked this article, Julie suggests the following products to help you continue the work with your horse (or call 800-225-8827 for ordering help):
GPR, vol. 4, Canter with Confidence: http://shop.juliegoodnight.com/shop/trgpr4canterwithconfidence.html
blog 
youtube 
