A whore bath is just where someone takes a sponge bath using water from a sink, bowl etc.
It means they don't actually get into a bathtub or shower to fully wash up but instead they just fill a sink or bowl with water and soap and then use a washcloth or sponge to wash themselves down.
In simple terms the whore bath is just the same as a sponge bath.
My Grandma used to call the sponge baths she had given to her at the nursing home a whore bath.
The nurse was like what the heck do you mean a whore?
She explained to them that it didn't mean that the nurse was a whore it was just what she heard of sponge baths being called.