In sub-tropical Australia where I was working 99-03 mobile dog wash vans were common sights.
Hi-Ace van models that let you easily stand up in it, and interior tub set to a height easy to bathe a dog.
Dogs would get pretty ripe in sub tropical heat, and if not bathed regularly, some breeds could develop skin conditions.
So it was a booming business.
They would pull up to the curb at the house.
Run a long hose in to the outside water tap on the house.
(Tap water was never cold there.)
Then run a long power cord to a power socket on the house.
Rinse water would drain to the curb
(and often evaporate before it made it more than ten houses down the low direction).
Never heard of them operating as mobile rub and tugs.
But I suppose that would be an added service fee to just the services rendered for the real pooch cleansing.