His power only works in his forest. Outside it he would be no better than a common man.

And even him wouldn’t be able to destroy the ring by himself, even on his forest.

In the books Gandalf and Elrond dicuss having Bombadil take the ring, or hide it in his forest. It would just slip his mind and end up worse than before

Quote from the book

No,’ said Gandalf, ‘not willingly. He might do so, if all the free folk of the world begged him, but he would not understand the need. And if he were given the Ring, he would soon forget it, or most likely throw it away. Such things have no hold on his mind. He would be a most unsafe guardian; and that alone is answer enough.’