[Overtaxed]

I would assume Tom B. was one of these Ainur, who were called the Maiar.

I thought that the Maiar were beings on the same "level" as Gandalf, Saruman, and Sauron all of whom were affected by the ring. Bombadil seems to have powers greater than these (or at least greater than Gandalf and Saruman.)

[Restorer]

Tom B. could be a Maiar, just one of a different "type." His power is limited to a very small area, the Old Forest, but in that area it is very concentrated and therefore powerful. In some of Tolkien's unpublished tales, he portrays Middle Earth itself as Melkor's "Ring." He sinks his power into it and into his armies and slaves to gain control over them. But then he is faced with the dilemma that his power is widely dispersed and he may be unable to concentrate it in time when needed.

Tolkien's implication is that this is why the Host of the West is able to fairly easily defeat Melkor/Morgoth at the end of the First Age. He has sunk so much of his power into controlling Middle EArth that he has little left to fight the attacking Host.

Maybe Tom B has gone the other direction. His originally much lesser power is so highly concentrated that it is able to resist even the power of the Ring.

Also, I see his resistance to the Ring as not one of power so much as one of attitude. He just doesn't care about what the Ring can tempt him with.