Una -- we use Bosu balls at the gym all the time and there is almost nothing you CAN'T do with one! Some of my faves:
1. Step ups. Put the ball against the wall, put the palms of your hands on the wall, put one foot on top of the ball, and just step up and down with the other foot. (I.e. right foot on the ball, left foot steps up on the ball, back on the floor, lather, rinse, repeat.)
2. Push-ups. Put either your hands or your feet (or your knees) on the ball and knock yourself out.
3. "Swimming." Lay on your back, hold the ball (flat side down) over your chest. Lift both feet about 6-12 inches from the floor and kick like you were swimming, without touching the floor.
4. This one is hard to describe, but I will do my best. Stand beside the ball, and sort of skip from side to side. If you start on the right side of the ball, you skip left and put your left foot on the ball briefly, then quickly replace it with the right foot, then your left foot lands on the floor. Kind of a step-together-step movement. You're going up on the ball, then down to the floor, in a sideways movement. This one will get your heart rate going FAST!
5. Wall sits. Put the ball against the wall, stand on the ball with both feet on the top and your back against the wall. Bend your knees until only your butt is on the wall. Hold until you scream.
6. With the ball against the wall, stand on the ball facing the wall, put both hands flat on the wall at chest height, bend your knees, and alternate stamping your feet as fast as you can: left right left right left right. Try to do it hard enough so you can hear your footsteps. Trainer Dave always says "try to pop the ball!"
7. Bridges. Lie on your back on the floor, put your feet on the top of the ball, hands at your sides with palms on the floor, butt close to the ball, and lift your butt as high as you can -- ideally only your shoulders should be on the floor as you "bridge."
8. Crunches. Sit on the ball, just below the top, knees bent and feet flat on the floor, and do your crunches.
9. Planks. Put your forearms on the ball and your toes on the floor, or your toes on top of the ball and your forearms on the floor, keep your body straight and parallel to the floor, and hold. You can also do this as a side plank with one foot stacked on top of the other foot.
10. "Superman." Get on your hands and knees on the floor with one knee on top of the ball. Lift the leg that is not on the ball so it is straight out behind you, level with your back. Foot flexed, pushing back with your heel. Lift the opposite arm so it's straight out in front of you, thumb up. All your weight will be on the leg that is on the ball. Hold. Switch sides, repeat. If you want a real challenge, try to lift your toe off the floor and just balance on your knee.