[Meneltarmacil]

Getting back to the original topic, I think that it would be hard for Bilbo, unaccustomed to sneaking around unseen, to have stayed completely undetected until he had jumped right over Gollum's head, as Gollum was probably a lot more familiar with his surroundings and was very well accustomed to seeing things in the dark. Also, the reactions from the Goblins (they saw him, then they didn't see him as soon as he put on the Ring) immediately afterward should make it clear that the Ring's powers were real and not just part of a "placebo effect" which only Bilbo would have experienced.