In "The Fellowship of the Ring," when explaining the story of the Ring to Frodo, Gandalf says, "I wondered often how Gollum came by a Great Ring, as plainly it was -- that at least was clear from the first."
Gandalf doesn't explain his reasoning, but he is definitely claiming to have known "from the first" that Bilbo held a Great Ring. Gandalf knows the whereabouts of the Three (he himself holds one), so at this point he has already pegged Bilbo's as being one of the Seven, one of the Nine, or the Ruling Ring.
And later, quoting Saruman in some past conversation: "The Three, the Seven, and the Nine had each their proper stone. Not so the One. It was round and unadorned..."
At this point, Gandalf had all the information he needed to identify the Ring. Yet it wasn't till Bilbo's birthday party that he took up the search in earnest, and he still spent seventeen years confirming his suspicion before acting. WTF, dude?
(I classify this as a ridiculous nitpick because all you have to do is replace "a Great Ring" with "one of the Rings forged in the Second Age" or some such -- allowing for Bilbo's to be one of the lesser Rings -- and it fixes everything. Tolkien just muffed one sentence in a work of immense scope and complexity; and it was one of very few errors. I mean, you can trace the logistics of Mordor's assault on Gondor and Rohan's race to defend it, with supply chains and armies advancing on multiple fronts, and everything hangs together perfectly. But that one throwaway line still bugs me.)