It's simply amazing and both terrifying how fast a fish, be it a shark (non-nurse shark) or a barracuda or another marine predatory fish can strike so blindingly fast, they can turn and strike so quickly you have absolutely no defense and are in fact defenseless to their attack, there is just no reaction time to do anything and it's scary when you experience it and realize how defenseless you are.
You described a 'bump' which is disturbing if that is really what it was, or was it a failed strike at the fish that was near you? Typically it seems that when a shark bumps before biting something that indicates he was targeting what he was biting and the following bites were not accidental. The bump has been described by many bite victims as the precursor to the attack, indicating the shark is 'tasting' what he is thinking about biting.
If the shark did actually bump you prior to the bites this story is quite different then just a being in the wrong place while a shark was trying to attack a fish that was using you as cover.
Your description is confusing at what bit you, as part of it sounds like a nurse shark and part of it a non-nurse shark. A nurse shark is relatively slow and clumsy, almost dog like in their demeanor and certainly don't make lightning attacks, a nurse shark would more likely swim up to you and almost cling to you trying to get at a fish, you'd likely be pushing it away from you to get it away like "what the hell? Get off me!" Part of your description describes this almost exactly. But the other part about it making a lighting fast turn and striking you is not nurse sharkish at all, a typical reef shark or bull shark would certainly strike like this, with you never being fast enough to touch it at all. Perhaps the adrenalin and freak out typical of something like this is making you give the speed of the attack some extra speed then it actually was, because if you pushed the shark off of you, that's nurse shark behavior all day, and a reef or bull shark simply isn't clumsy and unless the thing was in a frenzy already it simply is not going to strike at a fish with two people in the water, sharks are very timid and wary of people, a nurse shark on the other hand, they are kind of the dumb redneck cousin of sharks that aren't too b