The closest example that I can relate to the bard is the Bureaucrat class from Anarchy Online. The Bureaucrat had several abilities: namely, wearing shades and a suit and using suitcases as weapons. His primary ability, however, was to give "pep talks", which raised the fighting capabilities of all of his allies for a certain amount of time.
This is the case with the Bard Song. A bard's Bard Song can be any number of things: a motivational speech, a rallying cry, the blare of a trumpet horn, or, simply, the person's presence and commanding aura. Restricting it to "a guy strumming a lute" is positively silly.
As for magic, the red dragon blood idea is the most prominent reason for bardic magic. It could also be the idea that the bard is simply born with a more natural understanding of the "rhythm" of the world, and is, thus, able to draw his or her power from it. Alternatively, it could be there simply to help make the bard's jack-of-all-trades motif more prominent. The choice is yours, I suppose.