As Gandalf stated at the Council. The Wise knew after attacking Dol Guldur that Sauron was searching for the One Ring. Saruman told them that the One was lost forever and Gandalf blamed himself for being lulled by those words. He had suspicions Gollum's ring that came to Bilbo was the One, "But I spoke yet of my dread to none, knowing the peril of an untinely whisper, if it went astray. Gandalf specifically said he told Aragorn about his suspicions about Bilbo's ring. It's not stated, but I am positive Gandalf would have told Elrond as well. It's implied that Gandalf let Galadriel in as well because word came to him from Lorien when Aragorn had captured Gollum.

So when when word came to Elrond from Gildor that Frodo Baggins, bearer of the mystery Ring was abroad as were the Nine out of the Blue, he put two and two together and guessed correctly that Bilbo's old Ring was indeed the One. And Galdalf was missing. Thus he sent out his most powerful people as soon as possible. At that point, there was little reason for secrecy. The Elves like Glorfindel that were sent out were among the most powerful in Rivendell - perhaps all were Calaquendi, the few survivors of the Rebellion left in Middle-earth. Glorfindel while probably not told before, I think, at least would have been fully filled in by Elrond before he left and I suspect all those who left Rivendell were as well. They would need that information to do their jobs and with the Nine already in pursuit there was little need for secrecy on that point.

Russ