Physics: in Unity, how can we implement the Bull Rider controller?

The question is definitely not specific enough. Are you talking about making a virtual rider and simply assigning the controller buttons from a generic USB driver to control the rider's balance? Begin by placing a vertical (human) rectangle on top of a horizontal rectangle (bull). Create random behaviors for the bull to tilt in each direction and turn. Then, create a game outside of it where you use the controller to apply a force in the opposite direction to balance it. Doing it using physics is not the easy way. You can encode the "answers" to the game, as if the tips of the bulls left, you have to keep the right for X seconds depending on the duration of the rollover animation, something like a Fast Time Event (QTE).