Also known as a pirate bath, a "Russian Bath" is a bath where you wash your arm pits, ass and genitalia in a sink generally with paper towels, a wash cloth, or just your hands. The term derives from a play on the term "rushing", not an ethnic slur.
He was late for his hot date, so he took a Russian Bath to make sure he wouldn't stink to high hell.
When a girl has her period on your hand while you finger her
Hey tom why is your hand all bloody?' 'Oh i just got a Russian Bath from Michelle