We've seen him several times, riding both his horse and a mule, and always make it a point to go to the rodeo when he's performing. The horse is just as honest at jumping on and off the rig as needed. He also "rode in the parade" with his horse atop the trailer.
The bison are well trained, but if you watch carefully, you'll note that he lets them settle for a couple of minutes before he starts working them. This isn't always apparent in youtube videos, but when you see him in a live performance, he waits until the bison are ready to work. After they've rolled, looked around, and whatever else they want to do, they do their part of the routine with little or no urging. We've seen the bison jump up on the trailer of their own accord.
There used to be a performer who did a simple reining pattern aboard a bison - his changes were pretty clean, but his stops didn't rock the world!
"I couldn't fix your brakes, so I made your horn louder."