I am installing ship lap in my bathroom on an interior wall. Do I need to put anything between the studs and the wood I'm installing to stop moisture from getting behind the ship lap and mold from growing? Someone at Home Depot suggested stapling plastic sheeting up against the studs before installing the ship lap.

You could install a vapor barrier. 4-6 mil poly would work. On most interior walls it isn't really needed. However, to be safe, I would install on a bath wall .

Ship lap is nice but if you are going to put it in a bathroom, I would never close the door when the shower is on. Even if there is a window and an exhaust fan.

Plastic behind it merely moves the area of condensation closer in. The back of the ship lap can easily collect all that moisture. Any nails that aren't stainless will eventually rust and pop and split the wood, and rust stains will run down...
But that's just me. I want renovations to last for at least 50 years.

I would not install ship lap in a washroom at all. The back side of the boards will still absorb moisture.