I'm not an instructor but I was always taught that if I was in any doubt or in any way unhappy to go around... which would have been a bit difficult for you if you haven't been taught how to do them!
I am a bit surprised that if the bounces were hard enough that you had to stop and inspect the aeroplane that the instructor didn't take control and initiate a go around or at least attempt to sort out the landing. However, as I say, I am not an instructor and not being there at the time makes it very hard to judge the actual situation.
