[Maédhros]

I do think 20 rings do not count as many, but that's not very important here. I assume Gandalf had more things to do than hunt for info on the ring Bilbo possessed. It probably was not the top priority on his list at first. Also, he probably didn't know where to exactly find the information he needed. Maybe he first went to Rivendell, then to Lórien and finally to Minas Tirith. We neither do know how large the archives were he had to search through. I assume they were after some 3000 years rather huge, and probably not as nicely inventoried as modern archives. Remember also that he didn't get easily access to Minas Tirith's archives of Denethor. All these things would have cost consideral time

Look at this:
From LOTR:

‘When did I first begin to guess?’ he mused, searching back in memory. ‘Let me see - it was in the year that the White Council drove the dark power from Mirkwood, just before the Battle of Five Armies, that Bilbo found his ring. A shadow fell on my heart then, though I did not know yet what I feared. I wondered often how Gollum came by a Great Ring, as plainly it was - that at least was clear from the first. Then I heard Bilbo’s strange story of how he had “won” it, and I could not believe it. When I at last got the truth out of him, I saw at once that he had been trying to put his claim to the ring beyond doubt. Much like Gollum with his “birthday present”. The lies were too much alike for my comfort. Clearly the ring had an unwholesome power that set to work on its keeper at once.

That was in the year 2941 TA.
From the Council of Elrond

'Some here will remember that many years ago I myself dared to pass the doors of the Necromancer in Dol Guldur, and secretly explored his ways, and found thus that our fears were true: he was none other than Sauron, our Enemy of old, at length taking shape and power again. Some, too, will remember also that Saruman dissuaded us from open deeds against him, and for long we watched him only. Yet at last, as his shadow grew, Saruman yielded, and the Council put forth its strength and drove the evil out of Mirkwood and that was in the very year of the finding of this Ring: a strange chance, if chance it was.
`But we were too late, as Elrond foresaw. Sauron also had watched us, and had long prepared against our stroke, governing Mordor from afar through Minas Morgul, where his Nine servants dwelt, until all was ready. Then he gave way before us, but only feigned to flee, and soon after came to the Dark Tower and openly declared himself. Then for the last time the Council met; for now we learned that he was seeking ever more eagerly for the One. We feared then that he had some news of it that we knew nothing of. But Saruman said nay, and repeated what he had said to us before: that the One would never again be found in Middle-earth.
` "At the worst," said he, "our Enemy knows that we have it not and that it still is lost. But what was lost may yet be found, he thinks. Fear not! His hope will cheat him. Have I not earnestly studied this matter? Into Anduin the Great it fell; and long ago, while Sauron slept, it was rolled down the River to the Sea. There let it lie until the End."'
Gandalf fell silent, gazing eastward from the porch to the far peaks of the Misty Mountains, at whose great roots the peril of the world had so long lain hidden. He sighed.
`There I was at fault,' he said. `I was lulled by the words of Saruman the Wise; but I should have sought for the truth sooner, and our peril would now be less.'
`We were all at fault,' said Elrond, `and but for your vigilance the Darkness, maybe, would already be upon us. But say on!'
`From the first my heart misgave me, against all reason that I knew,' said Gandalf, `and I desired to know how this thing came to Gollum, and how long he had possessed it. So I set a watch for him, guessing that he would ere long come forth from his darkness to seek for his treasure. He came, but he escaped and was not found. And then alas! I let the matter rest, watching and waiting only, as we have too often done.

` "The Nine, the Seven, and the Three," he said, "had each their proper gem. Not so the One. It was round and unadorned, as it were one of the lesser rings; but its maker set marks upon it that the skilled, maybe, could still see and read."
`What those marks were he had not said. Who now would know? The maker. And Saruman? But great though his lore may be, it must have a source. What hand save Sauron's ever held this thing, ere it was lost? The hand of Isildur alone.
`With that thought, I forsook the chase, and passed swiftly to Gondor. In former days the members of my order had been well received there, but Saruman most of all. Often he had been for long the guest of the Lords of the City. Less welcome did the Lord Denethor show me then than of old, and grudgingly he permitted me to search among his hoarded scrolls and books.
' "If indeed you look only, as you say, for records of ancient days, and the beginnings of the City, read on! " he said. "For to me what was is less dark than what is to come, and that is my care. But unless you have more skill even than Saruman, who has studied here long, you will find naught that is not well known to me, who am master of the lore of this City."

This is sad. Gandalf had a hunch in 2941 TA that there was something odd with Bilbo's ring. But he had to wait until 3001 TA to seriously think that it could be Sauron's ring. There had passed 60 years. It is in 3017 TA that Gandalf goes to Minas Tirith to read the scroll of Isildur.
If Gandalf had been more vigilant, he could have just travelled to Minas Tirith circa 2942 to find out about the One Ring, so as to discard that it was not Sauron's ring, instead of waiting 75 years to do that. And a minor plus point is that probably Gandalf would have been better received by Denethor at an earlier time.

Another thing to consider is, that the Elves and Woodmen fighting the Orc party who had attacked Isidur's group probably left quite quickly after destroying and pursuing what was left of the Orc party.
Gondor and Arnor, moreover, were, just 2 years after the War of the Last Alliance and after Isildur's death in great turmoil, I assume, and the people were more interested in destroying what was left of Sauron's armies and in rebuilding their society than in searching for the remains of Isildur, which they thought had washed to the sea.

That is an horrible excuse. I wonder how many people could have been saved, if the Ring had been destroyed before Sauron had been able to regain his strength.
Why didn't Elrond do a decent search then, if he himself had warned Isildur to destroy the Ring? His realm was not in great turmoil. What is his excuse then?