The canter is an upwards motion. If you push your hips forward, your butt will get airtime and slam down, causing his little "rabbit" hops.
What helps is (and this may seem really backwards) stretching down and sitting back just a little so you are slightly behind the motion.
If you cling on for dear life, that's like squeezing a bar of soap.. it goes flying.. and so will you.
Relax.. it's not going to look pretty. Feel free to laugh it up at my canter videos
They are... pretty bad LOL.
Push the horse forward into the bridle.. regardless of English or Western.
See if they'll pop you on the lungeline. Riding without your hands is very helpful. Cantering is really fun once you learn to relax :)