Known as "Rudy the Rifle" for his uncommon arm strength, he tied an NFL record with 13 consecutive pass completions in the 1964 season.

He was starting quarterback in his senior year at Roosevelt High School, a team that did not win a game.

After the Trojans' primary passer, All-American halfback Jim Sears, was sidelined early in the first quarter with a broken leg,[4] Bukich came in and conducted a drive, completing all but two of his passes, that resulted in the only score of the game, and USC defeated Wisconsin, 7–0.

He was a reserve quarterback with the Bears in 1963 when they won the NFL championship (Bill Wade was the starter throughout the season).

[2] In his later years he was diagnosed with chronic traumatic encephalopathy (CTE), and he died at age 85 in San Diego in 2016.