Sometimes Maia is the term, sometimes Maiar; I think Maia is the singular.
Now Bombadil, that is a different story.
Suddenly he stopped. There was an answer, or so he thought; but it seemed to come from behind him, away down the path further back in the Forest. He turned round and listened, and soon there could be no doubt: someone was singing a song; a deep glad voice was singing carelessly and happily, but it was singing nonsense:
Hey dol! merry dol! ring a dong dillo!
Ring a dong! hop along! fal lal the willow!
Tom Bom, jolly Tom, Tom Bombadillo!
Of the many spirits that descended into Arda at its beginning, those of lesser stature than the Valar, though they were still powerful, were known as Maiar. Each of the Maiar was attached to the 'people' of a particular Vala. So, for example, the Maia Ossë, as a spirit of the sea, belonged to the people of Ulmo, while Curumo, the Maia who came to Middle-earth as Saruman, belonged to the people of Aulë the Smith.In the Third Age, there were still Maiar in physical form to be found in Middle-earth. The most important of these were Saruman, Sauron (originally also of Aulë's people), and Olórin, known as Gandalf, who belonged to the people of Manwë and Varda.