system
Given the following post, respond as if you're commenting on Reddit:
human
[Hobbit] How did Sauron or the Nazgul not see/sense Bilbo when he uses the ring in the Hobbit?

Or for that matter Gollom for all the time he had it. When the dwarves are captured by the wood elves in the Mirkwood forest, Bilbo spends days if not weeks wearing the ring. Yet every time Frodo even *thinks* about putting on the ring he is instantly a target and everyone knows where he is…?
gpt
The films are... different. Sauron only knew where Frodo was on Amon Hen, and when he claimed the Ring inside Mordor. Amon Hen was sort of a weird place, which encouraged farsight but also apparently made you "stick out" more to those with farsight of their own. That plus the Ring meant that Sauron found him -- albeit not enough to identify him, thanks to the intervention of either Galadriel or Gandalf. And claiming the Ring was directly challenging Sauron in his own land, so it was more the claim than the use of the Ring that drew the attention of Sauron.

Bilbo never outright, knowingly claimed it as his own and challenged Sauron for its ownership. Neither did Gollum (though he likely would have done so given the chance). Use of the Ring never functioned as a homing beacon for Sauron. The films changed this to make some things easier to show visually and enhance the menace of the Ring. But, for example, Sam uses the Ring for an extended period in the Pass of Cirith Ungol, following around orcs and evading Shelob. Sauron never notices that.