Bub may have been short for Bubba. I knew a fella that everyone called Bubbie. Years later I was told that it was common back in the day for the oldest son to be called Bubba or some form of that. It started with the younger siblings. Parents would refer the older their brother simply as "your brother". And, when the siblings were very young they would call the older brother "Bubba" because that was how they pronounced "brother". And, the parents just picked up on it and it would stick. Similarly, the oldest girl would be "Sister" or "Sissy". My mother and her next oldest sister always referred to the oldest (of 3) sisters as "Sister" until the day they passed.