De O Senhor dos Anéis livro 1, Capítulo 2: A Sombra do Passado :
"The Ring of Power looks after itself, Frodo. It may slip off treacherously, but its keeper never abandons it... It was not Gollum, Frodo, but the Ring itself that decided things. The Ring left him...
"There was more than one power at work, Frodo. The Ring was trying to get back to its master. It had slipped from Isildur's hand and betrayed him; then when a chance came it caught poor Deagol, and he was murdered and after that Gollum, and it had devoured him. It could make no further use of him: he was too small and mean; and as long as it stayed with him he would never leave his deep pool again. So now, when its master was awake once more and sending out his dark thought from Mirkwood, it abandoned Gollum."
Então há a motivação para por que o anel deixou Gollum: Sauron estava chamando, e Gollum era inútil. Quanto a como , sabemos de o Hobbit que Gollum ocasionalmente deixou sua piscina escura, usando o anel, para que ele pudesse se esgueirar em orcs (chamados "goblins" na minha copiar) e matá-los para comer. Provavelmente foi em uma dessas excursões que o anel saiu de Gollum, razão pela qual Bilbo achou tão longe da piscina.
Sobre o mecanismo pelo qual o anel abandonou Gollum, do mesmo capítulo:
"[Bilbo] had found out that the [ring] needed looking after; it did not seem always of the same size or weight; it shrank or expanded in an odd way, and might suddenly slip off a finger where it had been tight."
Foi assim que o anel originalmente traiu Isildur, e teria sido assim que ele finalmente saiu de Gollum: expandindo no momento oportuno e caindo direto de seu dedo.