The Middle Distance

Well, it's canon in The Hobbit that neither Elves nor Dwarves can see Bilbo when he's wearing it, so the effect definitely works in that direction - now, would a powerful Elf turn invisible while wearing it? I don't know - but I think it's implied that the fact that Bombadil doesn't is something very shocking and weird. Has any Elf or Dwarf ever even tried it on? Maybe not. That's an unknown factor, then.