Slight diversion - bluebirds, as in Vera Lynn and the white cliffs of Dover - there are no such thing, not in the UK at any rate. Bluebirds that is, not white cliffs. The white cliffs exist and I've seen them.
The song was written by 2 American song writers. There are bluebirds in America so perhaps the song writers didn't know that there were none in England.
I guess you could sing a more ornithologically accurate version but I suspect it wouldn't scan quite so well. Martins perhaps? Or swallows? Ah well, poetic licence and all - I guess everyone knows what it means, even if they don't.