I'm glad you've asked this question as it's fairly a common problem and we've not yet posted an answer to the horse that bucks when asked to canter.
This is usually caused by a couple different things. So often we suddenly yell at the trot " CANTER," and kick the horse hard, then freeze up and pull back on the reins. The horse is all confused and even gets nervous. A lot of horses buck and some crossfire - cross canter. Let me offer a few suggestions.
Begin by making absolutely certain that your saddle is not causing pain. This is easily accomplished by eliminating the saddle and riding bareback. If the horse doesn't buck - voila! Be absolutely certain you give the horse plenty of rein when you ask for the canter. But don't suddenly ask, instead allow the horse to find it by pushing right through the trot. In other words just push the horse faster and faster until he just naturally takes the canter. A great exercise to get the horse prepared is to drive the horse at liberty in the round pen, first without the saddle, then with. Watch as the horse just drifts right up through the gaits and takes the proper lead - front and back. When the horse can do this well in each direction, first without the saddle, then with, then it's time to ride. Stay out of the horse's way (mouth). Grab mane if necessary so you are with the action. Just allow the horse to take as many strides at the canter as he wants, then drift back to the trot. Lavish praise will tell him he did the right thing. That's stroking on the neck and using kind tone of voice. DON'T SLAP HIM ON THE NECK WHEN HE DOES IT RIGHT, INSTEAD STROKE HIS NECK.
Now if everything seems to be OK and he still needs to buck - probably a crow-hop, just bump his head back up with one rein and a shhhhhhhhhhhh noise. He'll find it uncomfortable to get his head down which he needs to do to really buck. Remember, there is a loving zone I call the " white zone" and an uncomfortable zone that is no fun called the " black zone." Make it all very obvious and you'll probably succeed.
Be certain you've warmed him up and done some groundwork before rushing into the round pen. Chances are, you, like most riders, do very little work to prepare the horse to ride. This is what my program is all about- preparing the horse for the ride. It's called Frank Bell's 7-Step Safety System and will give you a step by step to learn the #1 absolute most important survival tool - THE ONE REIN STOP. If you take a little time before the ride and apply these simple exercises, you'll take 80-90% of the risk out of the ride. Do you like those odds? If so, read the three Western Horseman articles at the news/press link. I've made my system so accessible via my foundation video, " Discover the Horse You Never Knew," audio book, laminated pocket card, and of course, the written word.
Let me hear from you Lori after you've applied these principles.