[Westerly Wizard]

The one ring was originally included in the Hobbit merely as a means for Bilbo to escape from Gollum's lair. Thus, it would not very serve this purpose if Gollum could see Bilbo with the RIng on (thus there isn't really a need for concern over the issue). The more meaningful concern is why Gollum can see Frodo and Sam cannot (which can be answered pretty easily).

If you want a reason for the difference, it may be hard to find because it wasn't of importance (although perhaps Tolkien, the nitpicker that he was, had one in his mind). A possible explanation might come from the idea that when someone was in sunlight with the Ring on, peopel could still see their shadow (as explained in The Hobbit). When Bilbo has the ring on underneath the mountains, it is extremely dark, so no shadow. But when Frodo has the Ring on at Mount Doom, he is standing in front of a fiery pit, so there is light. Gollum, having lived half an age in the dark, would possibly have the ability to make out a shadow easier than Sam.

Personally though, I think Gollum is only able to see Frodo due to his total obsession with the Ring and because he wore it so long. Like the Nazgul are drawn to the ring, so is Gollum (which is why he left the mountains for Mordor). Bilbo does not claim the Ring for his own, but Frodo does, so therefore Frodo is drawn to it like he was to Mordor, and the drawing is strong because they are at the location of the Ring's forging.

Another reason that Gollum could see Frodo but Sam can't is because Gollum has worn the Ring for so long, he now lives partly in the Wraith world that the bearer enters into when he puts on the Ring (like the Nazgul do entirely). Thus, Gollum can still see Frodo.