[JennyHallu]

I think he assumed Bilbo was dishonest.

Bilbo had, after all, just cheated on the Riddle-game. And he had been clever enough (ok, lucky enough, but how does Gollum know that?) to steal the Ring. And Gollum had not had contact with anything more intelligent than a fish for a long time. He could only have predicted Bilbo's actions based on what he himself would do. And he would have lied. I always figured that Gollum believed Bilbo only came down to his pool in order to deliberately steal the Ring. Paranoid little guy...