The ring was only as powerful as its owner

[Witch King of Angmar]

I've recently been rereading the Hobbit and I was wondering that. I think that Sauron was not looking for the ring yet and he was still trying to restore his power to full. And if he was I do not think he would think to look so close to home, as was displayed in the LOTR, but that's another scenario completely.

Another reason I think as is discussed above is the pull of the ring. It did not pull on Bilbo so much because Bilbo was not as easily corrupted. But if he was and his power were greater and he greatly tapped into the rings power, then the ring would have been easily sensed because of the power. But since the ring was used so scarcely used and when it was it was not tapped into greatly, it was difficult to spot.

When the ring was idle it could not be detected as is seen when it feel in the river for God know how long.

One thing else, think about the bearer, a Hobbit. The Hobbits showed nothing but incredible strength. All the times Bilbo helped the Dwarves. When Frodo was cut by the knife of the Nazgul he lasted as was stated by Gandalf longer than would be expected by anyone. That was a grave wound that haunted him for years after it was inflicted. There was Merry and Pippins valor in battle also.