One Ring Futility / Unwanted Bilbo

[CAB]

They saw him sooner than he saw them. Yes, they saw him. Whether it was an accident, or a last trick of the ring before it took a new master, it was not on his finger. With yells of delight the goblins rushed upon him. - The Hobbit

‘Though he had found out that the thing (Ring) needed looking after; it shrank or expanded in an odd way, and might suddenly slip off a finger where it had been tight.’
‘Yes, he warned me of that in his last letter,’ said Frodo, ‘so I have always kept it on its chain.’ - Gandalf and Frodo in the Fellowship of the Ring

It would seem that the Ring was trying to leave Bilbo, just as it left Isildur and Gollum. I would guess it didn’t have too many opportunities while Bilbo was in the Shire, there just weren’t enough Orcs running around.

Another thing, not to put it too bluntly, but the Ring kind of sucks at getting lost by an unwanted holder and getting found by Sauron’s servants, doesn’t it? First it falls off Isildur’s finger in the middle of a river. Then it falls off Gollum’s in the Orcs’ cave (probably its best effort) only to be found by Bilbo. When it first tries to lose Bilbo it only finds the bottom of his pocket (see the quote above). Also, I would guess that when Sam (actually, the Ring) frightens off the Orc in the tower of Cirith Ungol, this was actually the Ring calling for the attention of Sauron and his servants.