Was the One Ring destroyed?

[Hookbill the Goomba]

I think the desire of The Ring was still apparent in the world to those that bore it. Bilbo (bar Gollum and possibly Sauron if we are going to be pedantic) bore it the longest and after its destruction, he still asked Frodo, "What became of that old ring of mine?" It quite obviously still bears on his mind. Perhaps because he bore it as it's power waxed and so it's influence grew on him, even after leaving it.
That's just the way I saw it.