Bouncing does two things. It gives your body upward momentum. Also, if done every time you get on your horse, it "warns" them or tells them you are getting on and they can better balance themselves. At least that's what I think.
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That may well be right giving the horse a que when mounting. However in the case of the older generation some of us don't have any bounce fore getting on, or for when we fall off.
My horse knows when I rock the saddle from side to side I'm letting him know I am about to try and get on so he has the time to brace himself. He also knows it may be another five minutes and several attempts before I manage it.