I'm sorry I have to mix a little movie line with The Hobbit the novel.
In Peter Jackson's The Fellowship of the Ring, Lady Galadriel, while narrating the beginning of the movie, mentions that the the One Ring "abandoned Gollum" and the ring is shown bouncing down a slight incline, as if propelling itself to get away. I realize this is not canon.
In The Hobbit, here's how Bilbo finds the ring; it's really rather mundane!
[He] crawled along for a good way, till suddenly his hand met what felt like a tiny ring of cold metal lying on the floor of the tunnel. It was a turning point in his career, but he did not know it. He put the ring in his pocket almost without thinking; certainly it did not seem of any particular use at the moment.
The Hobbit -- page 68 - Del Rey Paperbacks - chapter 5, Riddles in the Dark
Later in the book, Gollum has his freakout:
Suddenly, [Bilbo] heard a screech. It sent a shiver down his back. Gollum was cursing and wailing away in the gloom, not very far off by the sound of it. He was on his island, scrabbling here and there, searching and seeking in vain.
'Where iss it? Where iss it?' Bilbo heard him crying. "Losst it is, my precious, lost, lost! Curse us and crush us, my precious is lost!'
The Hobbit - page 82 - Del Rey Paperbooks - chapter 5, Riddles in the Dark
Did Gollum himself lose the ring in the cave? Did the One Ring, hearing the call from its master Sauron, manage to move itself through Gollum's lake to the land?
How did the One Ring physically abandon Gollum?