"Bud"is a common nickname and term of address. Same as "buddy." Gaelic has nothing to do with it.


https://www.openculture.com/2013/03/hear_zora_neale_hurston_sing_the_bawdy_prison_blues_song_uncle_bud_1940.html



"The song comes from experiences with the infamous Chief Transfer Agent for the Texas prison system, 'Uncle Bud' Russell, whose dreaded wagon, 'Black Betty,' was possibly the reference for a work song immortalized by Lead belly, no stranger to Texas prisons (Russell also gets a name-check in Lead Belly’s 'Midnight Special')."