Informal, friendly generic word used in place of a proper name like Buddy. Bubba as "Brother" is used especially by Southerners, Westerners and Black Americans (and small kids who can't say "brother") as a friendly or familial term thus Baby Bubba is the same only more so. Doesn't have the possible misunderstanding of disrespect of Bubba by someone who looks down on southerners.
What's up Baby Bubba? Where you been hiding yourself?