We have just begun working on a property that conducts trail rides and have a horse here that we discovered to have the problem of bucking. After investigating this behavior, we also noticed that he hates any kind of contact on the reins and will begin to throw his head around to free himself up. He has a normal snaffle bit on his bridle. We found that while using him as a demo horse, he would grow impatient and begin to play up after being mounted, and while on trails will throw his head around and then buck when pulled up. In the arena when he bucks, we pull his head up and drive him forward, but we feel that this behavior could stem from his dislike of the bit. Do you have any suggestions that could help us to train him out of these habits?
There are so many things that could contribute to the behaviors that you describe, that it is hard to know where to start. The first and most obvious thing to consider on the head tossing is to have the horse's mouth checked for wolf teeth, tongue scaring or other dental problems that might be causing pain for the horse. It is also possible that an ill-fitting saddle or a back problem could cause bucking; so those things should be ruled out as well.
After ruling out a physical problem, then you must look to the horse's training. You do not mention how old he is or what his background is, but it is quite possible this horse has never really been formally trained. It amazes me how often people just start riding horses, without ever formally teaching the horse what he is expected to do. So many horses today are so willing and well tempered that it is pretty easy to just throw a saddle on and start riding. This will work fine for a while until the horse becomes frustrated or rebellious and then the holes in the training surface. Often, trained or not, horses become what I call "anti-trained," where people teach them the wrong thing, undesirable behaviors like if I buck, they'll let me stop or if I throw my head, they will loosen the reins. These behaviors usually develop out of a sense of self-defense for the horse who gradually begins to protest meaningless pressure on his mouth, back and sides.
The solution, whether the horse has been formally trained or not is to retrain him, starting with the basics, teaching him how to respond properly to the bit. I would do this in the round pen with a self-correcting bitting device that teaches the horse to give to pressure from the reins, both vertically (up and down) and laterally (side to side). Once he has learned that when he gives, the pressure goes away, then you can start riding him again and go through the same training process from the saddle. Of course, you'll have to make sure people are not inadvertently pulling on his mouth or pulling a constant contact on the reins for no reason (this is a very common cause of head-tossing).
With the bucking, it is possible that the two problems are related. Horses don't do anything without a reason and most likely the head tossing and bucking are forms of protest from the horse from being hit in the mouth and back. But it is also possible that the bucking is a refusal to go forward, so working on obedience and forward movement are important. I would suggest returning to some basic groundwork, round pen and lead line, to re-establish a respectful and obedient relationship with the horse.
Basically, if you can rule out any physical problems with this horse, what you need to do is start over with his training. Some how along the line, he seems to have lost his foundation, if he ever had one. Good luck!