Q: Why Did Sauron and the Nazgul Not Know When Bilbo Wore the Ring?
ANSWER: Some readers of The Hobbit ask why Sauron did not send the Nazgul to search for the One Ring when Bilbo was running around Mirkwood and Dale while wearing the Ring. This confusion has probably been exacerbated by the Peter Jackson movies, which make it seem as though Sauron was aware every time Frodo wore the Ring.
However, in the books Sauron was only aware of Frodo on one occasion: When Frodo sat on the High Seat of Amon Hen, which appears to have been imbued with “Numenorean magic”, he was able to survey Middle-earth in what seems a highly unusual way (Aragorn later sat on the seat and did not perceive nearly as much as Frodo). It was only when Frodo allowed his gaze to fall on Barad-dur that Sauron became aware of him and immediately began searching with some sort of “vision” for Frodo.
Now, it is true that J.R.R. Tolkien wrote that the Nazgul were drawn to the Ring — he even has Aragorn say as much. But the Nazgul were not equipped with highly calibrated One Ring Radar and it did not have a homing device attached to it. The Nazgul could only get a general sense of in which direction the Ring lay until Frodo began to fade or when he put the Ring on.
They were better able to perceive Frodo himself than the Ring.
Furthermore, Sauron did not send the Nazgul to look for the Ring until he learned that it had actually been found. Sauron apparently believed the One Ring had been unmade or lost forever until Gollum was captured and taken to Barad-dur. When Sauron learned from Gollum that he had possessed the Ring for several centuries, only to lose it to Bilbo a few decades previously, Sauron put into motion his plan to send the Nazgul to search for the Ring.
First, Sauron had to prepare and mount an assault on Gondor that would allow the Nazgul to cross the Anduin and begin their search. Tolkien does not explain why the Nazgul had to cross the river at Osgiliath (rather than at Cair Andros or the Undeeps), but according to Radagast they were asking about “Baggins” and “Shire” wherever they went. Perhaps they began asking questions in Gondor.
Hence, the mere fact that someone was wearing the Ring — especially hundreds if not thousands of miles away — was insufficient to make Sauron or the Nazgul aware of the Ring’s activity and presence. Sauron and his servants had to know the Ring was being worn and they had to be relatively close to the Ring to even sense it.
The Lord of the Nazgul appears to have sensed the One Ring as he led his army from Minas Morgul (when Frodo, Sam, and Gollum watched the army pass by), but he was not sure of what he felt. Do you really think he would have continued to attack Gondor if he realized he could have seized the Ring and brought it to Sauron right then and there?
The reader should not be surprised that Sauron could not simply locate the Ring whenever someone was wearing it. That would have made the story very different from the way it unfolded. The surprise and fear that Sauron felt at the very end, when Frodo finally revealed himself and claimed the Ring as his own, would have been greatly diminished if Sauron could have tracked the Ring so easily.