The main reason for using a bosu ball is to increase the number of muscles and muscle fibers recruited for the activity, and to increase the proprioception. I had to use the Bosu quite extensively for my Achilles rupture rehab, and here's a few the exercises that I was doing (My PT guys were creative sadists, but they were good.):
- Chop squats - Put the round side down, stand both feet on the flat. Take a medicine ball and "chop" (Much like a cable pull) from high to low, left to right and squat at the same time the ball comes down. Repeat going the other way for one repetition.
- One legged deadlift - Done with a swiss ball, stand on the rounded side, foot in the center. Holding the ball out in front of you, lean until it touches, then stand back up.
- Side touches - Standing on one foot on the ball side (not on the flat), stick your leg out to the side, squat until the toes touch, then back up.
- Net toss - Requires a large net that you can use to "throw" the ball back to you. (See picture below) : stand on bosu flat side, throw medicine balls into the net and catch coming back.
Other exercises that I did that would also help:
- Medicine ball slams - Stand with both feet together. Take a medicine ball and slam it into the floor on the right side of your body. Catch it on the way up, immediately rotate and slam it into the floor on the left side. 30 seconds of this x 3.
- Plate drags - Put a 35 or 45 plate flat on floor. Hook lip of plate with toes, and walk on hands forward 20-25 feet then backwards, pulling/pushing plate.
- Windmills - Take a 5-10 lb dumbbell in each hand. Stand on one foot, slightly leaning over. One dumbbell at shoulder height to side, other in front. Lift the one in front out to the side, at the same time you bring the other down in front of you. 20 reps, then switch feet.
All of these are designed to increase both the strength in the area, and the proprioceptive feedback.