That happened to me with Trigger when I bought him a new saddle the trea (tree) was too small for him and it really bothers them. He bucked me off and took off galloping and that was not at all like him! So I changed the saddle and now hes fine. Although he gives tiny bucks cause he's a brat it's not cause his saddle. Also if there blanket makes there hair stand up it also bothers them so make sure there hair is flat when you put the saddle blanket on and if you need to move it , I know its a pain but you will have to take the whole saddle off or it can cause discomfort causing the horse to buck. I'm glad your not severly injured. Talk to the owners of the stable and maybe a couple stable hands. But I'm like positive that, that is what it is. From the sounds of it anyways.
EDIT: Also from what I went through at my ridding stabel( a very supposidly good one but they are cruel to their horses) the people that teach lessons don't know much about the saddlery and other equipment, all they know is how to teach you.