Take great care with bleach bottles, and don't use wet hands. I know of an incident where a bottle of bleach slipped from someone's hands, hit the bottom of the sink, and the bleach shot up out of the bottle and into his face and eyes. He ended up in hospital where, fortunately, they were able to treat him successfully. Don't let it happen to you.
I find that the labels peel off in bits too. I usually just peel the whole thing off quite early on, saves me picking bits of soggy paper off my rubber gloves.