Summarize:

Most mechanical bulls are surrounded by bouncy, padded flooring. Use this padding to hop up and get your right or left leg over the bull. Then, use your hands and arms to steady yourself on top. Your legs should hang down on each side of the bull's back.  Some people might have trouble initially mounting the bull because it is too high. This is why you should use the padded flooring to your advantage. Try not to jump too high because you might miss and jump over the bull completely. Mechanical bulls will either have a padded strap or a long rope handle that you can hold on to. Use this after you jump up on the bull to stable yourself and adjust your positioning. It is best to hold on to it underhanded with your non-dominant hand. Holding on to the rope underhand allows for the best stability when the bull is in motion. It also helps you to release your grip more easily when you fall. It's best to position your body as far forward on the saddle as you can. This will help to minimize your movement, which will ultimately keep you on the bull longer. Once you are far up on the saddle, squeeze the sides of the bull with your thighs so you are firmly rooted to the bull's body. Position your legs forward and avoid angling them behind you when you're sitting on the bull. If your feet are behind you, it will be harder for you to balance while the bull is moving and you may fall forward on the bull if it moves down. Once your legs are positioned correctly, dig your heels into the sides of the bull and point your toes outward. This will allow you to get a better grip on the bull with your feet. Don't use your toes to try to hold on to the bull. They do not have enough strength to keep a good grip.
Jump up and bring 1 leg over the bull to sit in the saddle. Hold on to the rope palm up with your non-dominant hand. Move your body forward in the saddle and squeeze it with your thighs. Pull your legs forward. Dig your heels into the bull's side.