Simple enough. Gandalf's note opens with:
Bad news has reached me here. I must go off at once.
This is an obvious reference to Radagast's message to him from Saruman (relayed at the Council of Elrond):
"I have an urgent errand," he said. "My news is evil." Then he looked about him, as if the
hedges might have ears. "Nazgûl," he whispered. "The Nine are abroad again..."
Gandalf himself says shortly afterwards:
However, I wrote a message to Frodo, and trusted to my friend the innkeeper to send it to him.
So the "bad news" in Gandalf's note is the fact that the Nine were loose, and Gandalf's caution to not use the Ring is on account of fear of what the Nazgûl may do (as proved to be the case at Weathertop).
However, after Rivendell the Nine were unhorsed; again as Gandalf notes (in Many Meetings):
Their horses must have perished, and without them they are crippled. But the Ringwraiths themselves cannot be so easily destroyed. However, there is nothing more to fear from them at present.
It's also the case that after Rivendell Frodo was in powerful company: Elves, Men, Dwarves and Wizards. Before, and for all Gandalf knew at the time, he may have been travelling alone.
So the key difference is the Nazgûl - before Rivendell they were hunting for a relatively defenceless Frodo in the Wild, after Rivendell that was no longer the case.