I have a 1936 Los Angeles recording by Jimmie Davis of a song titled 'My Blue Bonnet Girl', but it seems to be different from what you describe. The attribution is to Davis alone, although Tony Russell notes that it was claimed by the songwriter Bonnie Dodd. The first line is:

From the wild coyote's howl where the little dogies prowled

The chorus is:

You can keep your violets blue
Keep your pretty daisies too
I don't want but one flower in this world
She's the fairest in the land
And I mean to win the hand
Of my sweet Texas blue bonnet girl

--Stewie.