Well, I'm not too knowledgeable about Child Ballads or how they're collected, but the Wikipedia page says they also collected their American variants, and that they were collected in the late 19th century, so it is possible it's referring to "the Bonnie Blue Flag" of the CSA. But I honestly doubt that.

But, in MUCH less hypothetical terms, "bonny" is a term of endearment and means attractive or beautiful, and I found a poem titled "The Blue-Eyed Lassie" by Robert Burns (Click) that mentions "the bonnie blue," obviously in reference to their love's blue eyes. So, depending on of Burns' poem came first or not, it could be an allusion, or even a popular term to call your loved one who may happen to have blue eyes (as many Scottish and English people do, which also happens to be where the Child Ballads were collected from).