Understand that a mechanical bull can do only three things: buck, spin and change direction. The key to riding a bull is staying centered, meaning your body is in the middle of the bull's buck and in the middle of the bull's spin.
Mount the mechanical bull. Wrap your hand around the rope or bar - depending on the mechanical bull. Get a good grip by squeezing tightly with your hand. Slide your bottom forward until your forearm is resting in the crook between your hip and your thigh.
Squeeze your legs around the bull. Turn your toes slightly out. This will allow you to use your hamstrings and gluteus maximus to hold on to the mechanical bull rather than just the inside of your thighs.
Flex your bicep. This will force the back of your forearm and your elbow down into the crook of your leg. Positioning your arm here allows you to leverage your hip to keep yourself centered on the bull.
Lift your off-hand in the air, bow your chest out and nod your head. When the bull begins to buck, keep your body straight up and down. Imagine a vertical line moving up from the floor, through the bull, through your hand and through your nose. If your head and shoulders move forward of the vertical line, you will fall off. It is almost impossible to fall off the back end of a mechanical bull. You will either fall off to the side or go over the front.
Maintain a straight up-and-down posture when the hind end of the mechanical bull bucks up. It will feel like you are leaning back. In reality, you are just sitting up straight as your legs move down. As the bull's hind end comes down, maintain your up-and down-posture by allowing your legs to move toward your chest.
Look inside the well as the bull spins. As the mechanical bull spins in a particular direction, turn your head and look in the same direction. Your head should be at a 45-degree angle from the center-line of the bull's spine. Look down. This is called looking into the well. It will keep your body centered to the inside of the bull's spin.
Turn the toe of your leg that is inside the well out slightly. Tuck your outside foot up against the bull, perpendicular to it. When the mechanical bull spins the other direction, turn the foot of your well-side leg out and tuck-in your outside foot. Deal with bucks and spins and changes of direction and you can master the mechanical bull.