You shouldn't be benching every workout. You should be squatting every workout. It's possible you got the SS workout from an incorrect source.
When benching, do you make sure the bar is over your wrist? Sometimes, the bar folds your hand backwards towards your chest until the mass of the bar is a few inches north (towards your head) of your wrists, and this places undue stress on them.
Other than that, taping the shit out of your wrists is the only thing I can think of.