Gollum's escape!

[Rumil]

I seem to remember that Gollum only knew that the name of Bilbo's homeland was the Shire (because Bilbo, rather foolishly, told him) but was just guessing as to its location.

It was perhaps understandable for Gollum to thik that the Gladden Fields were the Shire, as that's where he had come from many hundereds of years before when it was a thriving hobbit community. In Unfinished Tales, there's one version implying that the Hobbits were massacred by the Nazgul on their search for the ring, though that was later rejected.

Certainly Saruman knew where the Shire was and eventually told the Nazgul, though he had tried to conceal his information for his own ends.