Even with as much ambiguity that surrounds both the Ithryn Luin and Tom Bombadil, I think we know enough to rule out a connection.
The blue wizards arrived either with the other three wizards in the Third Age or in the Second Age with Glorinfdel before meandering into the east. Bombadil, on the other hand, was called "oldest" and "fatherless." He came before the rivers, trees, Kings, etc. per his own word - even "before the Dark Lord came from Outside."
Bombadil's immunity and indifference to the Ring (and Gandalf's familiarity with this) is also a sign to me. That's usually used as evidence that he wasn't a Maia of any sort, Istar or otherwise.
At the Council of Elrond, Gandalf reckons that "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."
Saruman was obviously obsessed with obtaining the Ring and its power. Sauron needed it back. Gandalf rejected taking it from Frodo for fear of becoming like Sauron. I think we can expect that Radagast, Alatar, and Pallando would all struggle similarly; the Ring would affect anyone and everyone.
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'No!' cried Gandalf, springing to his feet. 'With that power I should have power too great and terrible. And over me the Ring would gain a power still greater and more deadly.' His eyes flashed and his face was lit as by a fire within. 'Do not tempt me! For I do not wish to become like the Dark Lord himself. Yet the way of the Ring to my heart is by pity, pity for weakness and the desire of strength to do good. Do not tempt me! I dare not take it, not even to keep it safe, unused. The wish to wield it would be too great, for my strength. I shall have such need of it. Great perils lie before me.' (Book 1, Chapter II 'The Shadow Of The Past')
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Well, anyone but Tom.
Quote:
Then Tom put the Ring round the end of his little finger and held it up to the candlelight. For a moment the hobbits noticed nothing strange about this. Then they gasped. There was no sign of Tom disappearing!
Tom laughed again, and then he spun the Ring in the air - and it vanished with a flash. Frodo gave a cry - and Tom leaned forward and handed it back to him with a smile. (Book 1, Chapter VII 'In The House Of Tom Bombadil')
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Originally Posted by Galadriel55
Personally, I'm at peace thinking that I'm not meant to know TB's identity. He is, and that's all I need to know. 
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Three cheers!
"He is the Master of wood, water, and hill."
Tolkien was pretty adamant that "...even in a mythical Age there must be some enigmas, as there always are. Tom Bombadil is one (intentionally)." Of course, we can always continue speculation.