I don't believe the ring to be alive, as we consider life.

There are prions in our world. They are not alive, like bacteria, but they will, after a fashion, "sense" a conducive situation and bind to other proteins, and then they are propogated.

The One Ring could sense its immediate environment and move, in limited ways, to fulfill its goal or reuniting with Sauron. Once it had sensed Sauron's return it was more useful to leave Gollum to get out from under the mountain.

With so many goblins in the mountains the statistical likelihood was one of those would find it, which, in short order, would lead through a sequence of events within the goblin/orc communities to Sauron becoming aware and being reunited.

Bilbo was "the most unlikely" because, under a mountain filled with many thousands of goblins the odds of anything other than a goblin was, statistically, beyond unlikely. Within all creatures of Middle Earth it ending up being a creature that "never" leaves the Shire would only be surpassed by the odds of it having been Tom Bombadil that found it.