Sounds like it would have been an... interesting accident to have seen!
You could always go with a saddle sans stirrups, doesn't have to be bareback.
It sounds like it was your mounting technique rather than bareback riding - I know some people allow the horse a loose rein when mounting, but I'm all for ensuring control when I'm in that vulnerable 'limbo'. With or without a saddle. I would just ensure your horse knows how to respond to one rein held in 'neutral' - one rein stop, as opposed to one rein to turn - and just keep your nearest rein very short when mounting, so that if anything does go wrong, the worst he can do is circle, moving his rump away from you.