I presume then, that Tom Bombadil was destroyed when the One Ring went into the fire. Gandalf clearly hid this fact from the Hobbits by refusing to take them with him into the Old Forest. 'Away to see Tom' indeed!
Instead he sent them to the Shire all alone where they almost got themselves killed in a big battle.
Or maybe Bombadil wasn't destroyed, and the War betwixt Gandalf and Sauron continued into the Fourth Age.