In my mind Bombodil is akin to Yavanna, a Maia who decided to stay in Middle Earth ( as did Queen Melian ).
He perhaps set up his realm in the Old Forest as a kind of Nature guardian, a precursor to the Ents perhaps. Who knows, maybe his meeting with Goldberry and his love for her kept him in the Old Forest and changed his plan to be a protector. His claim to be Eldest is the conundrum, Eldest of what? That's the real question. Perhaps he forgot what and who he really was and simply thought he was the first speaking being on the Earth. Also it would have been thousands of decades before he met an Elf as per the location of The Awakening of the Elves and their eventual relocation towards the West. We need to remember that not even the Valar knew the exact date of wakening of the First Born. Lots of questions and that's what's best about the enigma Tom Bombodilo.