Neither Gandalf or Elrond ever exposed the fact that they were ring bearers until the Havens. Galadriel chose to let Frodo know that she had one. She'd even said that Sauron suspected that she was hiding one of them, not that he really knew for sure. Another reason being that Frodo never tried to use the ring for anything but to become invisible, he never attempted to see things, or use it in any other way.
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*~*Call me a relic, call me what you will.
Say I'm old fashioned , say I'm over the hill.
That old whine ain't got no soul.
I'll stick to Old Toby and a Hobbit hole.*~*
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