I have a couple tips, hopefully they're helpful. When I started cantering, I had the same problems. What I did is start with the half-seat canter. That's when you lean forward a little more than usual and stand up in your stirrups. Bend your arms to his stride so you don't hit your horse in the mouth with the bit. Move your hips with his stride.
Once you are comfaterable with that, sit back a little. Move your hands to his stride and rock your hips. You can also straighten you legs when you feel the bounce, and the bend them when you don't. It keeps you from bouncing so much.
As for your legs, squeeze with your thighs. The horse can't feel it so much because you're squeezing against the saddle, but it will keep you ballanced. Keep your legs still, and wrap them around the horse's sides.
Oh, and also don't let the reins flap around. Keep them nice and short. That way you can have good control over your horse and make sure that he doesn't speed up too much.
I hope I was helpful. :)