First, check your drain cover. If it has a screw in the center, remove it. Underneath you’ll see a cross bar that often collects hair and debris. Cleaning that out usually clears things up.
If that doesn’t solve it, try a non-caustic drain cleaner. Products like Drano or Liquid-Plumr are safe options, and you can usually find them at Walmart. They’re effective without risking damage to the plumbing.
I wouldn’t use a hair snake, though, as many RVs use a Hepvo waterless trap instead of a traditional P-trap, and a snake can damage it.