couldn't see Bilbo when he was invisible. To me that means that unlike
the High Elves (for example Glorfindel in LotR) they did not have a strong
presence in the spirit plane. Which means they would have been invisible
if they had put on the Ring. Glorfindel, on the other hand, did have a
strong presence in the spirit plane, and therefore would have remained visible
if he had put on the Ring.
The $64 question is whether Bilbo was invisible to Gandalf in The Hobbit.
Interestingly, we don't really know if he was or not. I suspect that
Gandalf could see him, but never let
on.
“I dislike Allegory - the conscious and intentional allegory - yet any attempt to explain the purport of myth or fairytale must use allegorical language. (And, of course, the more 'life' a story has the more readily will it be susceptible of allegorical interpretations: while the better a deliberate allegory is made the more nearly will it be acceptable just as a story.)” (From Tolkien Letter # 131.)