Why could Bilbo wear the Ring all the time but not Frodo?

Why could Bilbo wear the Ring all the time, but when Frodo did, they could finger him?

There are several differences between Bilbo and Frodo and the Ring to consider.

1) Time. Bilbo took possession of the Ring at the age of 50. He kept it for 61 years but used it mostly to escape unwanted encounters with obnoxious family members. Frodo was the given the Ring at the age of 33, kept the Ring for 17 years before leaving on the Quest. This equals 78 years in total. That is a lot of time. Just put it into perspective, today it is 2023, 78 years ago it was 1945. How much has changed from 45 to now? A lot can change and a lot did change in those 78 years.

2) Sauron. In the year Bilbo found the Ring, the White Council drove the “Necromancer”, who they had learned was Sauron, out of Dol Guldur and Mirkwood (this was the other business Gandalf spoke of as he left the dwarves and Bilbo at the entrance to Mirkwood). This was when Sauron “feinted” being driven forth but his minions had all ready for him in Mordor. For the next 77 years Sauron was very busy preparing for war. He knew the One was not destroyed but he did think it was lost, washed away down the Anduin into the Sea. So, for the 61 years while the Ring was held by Bilbo, Sauron did not actively look for the Ring. It was not until Gollum was drawn to Mordor that Sauron knew that his Ring was not lost. However, and this is key for you to understand, Sauron was not omniscient or omnipotent. He was not Eru Illúvitar. He was confined to being in one place at a time, not knowing all things, and unable to move about all of Arda at once (omnipresent). He was in actuality quite limited.

3) Distance. As Sauron was very limited in many ways, you must understand that the distance between the Shire and Mordor was about 1600 miles (about as far away as Nebraska is from Florida). This distance diluted Sauron's senses of the feeling of the Ring being used. And since Bilbo (and Frodo too) never used the Ring in the way it was meant to be used (to dominate others' wills and to rule Middle-earth) I imagine all the dark Lord felt was a tickle at the back of his mind (if even that) when the Ring was used.

4) The Nazgûl. The questioner states the word “they" so I am assuming he/she adds the Nine in with Sauron. The Nazgûl arrive on the scene in our story 78 years after Bilbo found the Ring and 17 years after Frodo received it. They were no longer in Mordor or even Mirkwood but in the Shire (and Bree, and the wilderness) nearby. In fact, they are right there, feet away, when Frodo puts on the Ring on Weathertop, and he stepped into their world. They could clearly see him! They could strike him with the Morgul blade. Up until that moment they did not know which Hobbit held the Ring. Putting on the Ring was exactly what they needed to pinpoint where the Ring was. The other time that Frodo was nearly “seen" by Sauron was a special circumstance.

5) Special Circumstance. Frodo put the Ring on and fled from a Ring-crazed Boromir and ended up on the Seat of Seeing, on top of Amon Hen. It was a magical place, and Frodo was wearing the Ring, a virtual psychic shout out to Sauron “here I am! I have your Ring!” It was also much, much closer to Mordor and even within “eyesight" so to speak. Frodo was very nearly discovered at that moment but unbeknownst to him, Gandalf saved the day.

So, there are many reasons why the Hobbits could put on the Ring, wear it as needed, unnoticed by Sauron, time, place, distance, special circumstances and the limitations Sauron himself lived with and by. All of these things things caused the differences between Bilbo and Frodo and Sauron and the Ring usage.