NO the pad should NOT be inside a plastic tub!!!!! This is sometimes necessary with wooden enclosures but typically covered with tiles or using a waterproof mat like a Kane.

Bleach inside a tub needs to be VERY carefully washed so NO smell of bleach remains. I'd recommend using something else if you cannot be assured of a perfect wash. Chlorohexadine, or a peroxide solution. That leaves a non toxic residue, I use a steam cleaner myself followed by a CHD rinse.