In Frodo's story, Bombadil is unique because he is immune to the Ring. So when Elrond says Frodo's story was strangest to him, it wasn't just because of Frodo's coming through, but also because of what dangers and helpers he met along the way. Bombadil is a logical thought to bring them around to Gandalf's question because of that immunity, and the question follows whether he could hide the Ring. That whole discussion is interesting, but we're not there yet.
I would imagine that after Aragorn and the hobbits arrived and told their story it became clear a council was needed. Legolas, Gloin and Gimli, and Galdor have all shown up with questions or reports that were related, so they were invited The elves from Elrond's household were summoned, I imagine. Boromir shows up just in time, also with a question relevant to the matter, so he is invited too. Elrond summoned some councilors, Gandalf summoned the hobbits and Aragorn, but fate brought the others.