I believe the old tradition of facing the back end of the horse to mount was that if the horse took off, you could swing yourself around and still get on. And, yes, that works if you are ready for it. Better than just standing facing the horse, or facing the head of the horse anyway. But, we are no longer, generally speaking, dealing with horses that are going to take off on us when we mount, so I think that mounting this way causes more problems than it prevents now.
I mount from either side, general facing the horse or slightly towards her head. I don't bounce, never understood the purpose of it, but then again, I have no difficulty at all mounting. I even used to get on my 17.x mare bareback without a block. (took practice, but I got it!)