I grew up near the Montana bison range ... big scary beasts! Basically lazy unless they see you as a threat and then they will stomp you into a greasy spot on the prairie.
Bison aren't really trainable, although a few exceptions have been trained to saddle, which is very hard to fit because of the shape of the critter. It would take generations of hand-rearing and rigid culling for temperament.
As for care, pasture or low-protein hay and access to water is all they really need.
They can, if they have to, move at a steady pace for miles and run a horse into the ground. They are extremely agile for their size, much more so than cows, and can charge 50 yards faster than a horse can run away. However, they are fairly herdable if you have riders advance slowly across a broad front ... they drift away from the riders. If you push them too hard they'll charge the horses and it gets ugly.
For a long time there was a battered WWII jeep at the gates of the refuge- some old bull took a disliking to it and stomped it into scrap metal. The refuge employee bailed out the back and hid in a ditch until someone came looking for him.
My dad watched them rounding up some bison on the refuge to ship somewhere (he was a kid, doesn't remember where the herd was going). The small herd went into the shipping corral at a brisk trot, led by a big bull, right up the loading ramp, where the bull lowered his head and continued at a brisk trot right through the reinforced sides of the railroad cattle car and back to the open range ... it's that kind of animal.
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Adding: A Mexican rancher I met was raising beefalo, and tried an AI cross between a bison and the breed used for bullfighting (toro de lidea). It was huge (about 2000-2500 lbs), solid black with a curly ringleted mane (not the fuzzy buffalo mane), and had a very aggressive disposition. The horns were larger than the usual fighting bull.