He is the father of J.D. and owner of Bud Dean Construction. Bud jokes that the company is more of a 'deconstruction' company, since most of the company's work is about blowing up buildings.
Not much is known on the specifics of Bud and his wife's relationship, but his wife killed her self using his work. She killed herself by walking into a library just minutes before Bud hit the switch to blow it up during their time in Texas. Her suicide heavily affects his relationship with his son.
His relationship with J.D. seems to be strained after the death of J.D.'s mother. Their relationship is a joking switch of roles. Bud will make jokes like "gosh, pop, I almost forgot to introduce my girlfriend" and J.D.'s response will be "son, why don't you ask your little friend to stay for dinner?".
J.D gets the idea of the bomb to blow up Westerburg High School when watching one of Bud's demolition videos. Bud is telling J.D. about how he had put a Norwegian bomb in the boiler room, which set off the thermals in the floors above. From there, J.D. builds the bombs to blow up the school.