Uh, no, actually I think Bird is almost guaranteed tease matieral. Thik of it: birdbrain, birdseed, bird-turd, birdshot/shit, Big Bird, flipping the bird... Not good.
I have known too old ladies named Birdie. One was named Birdie, as far as I know. The other had it asa nn for something, might be Bertha but I don't know for sure.
I don't think the song by the Be Good Tanyas is something that a lot of people would know about and associate it with the name.
Listen: Bird Lenore. Bird Manure.
Mr. Snuffleuppagus alwasy called Big Bird Bird too. As in "Oh Birrrrd."
I'd stick to using birdy type names like Jay or Robin. Or use it as a middle name and pretend it's a family name.
And if you like the Be Good Tanyas enough to want to commemorate them in a baby name, why not just use Tanya? That's a really cute name.