Bukich's greatest performances were during his second stint with the Bears in the 1960s. He was a reserve quarterback with the Bears in 1963 when they won the NFL championship (Bill Wade was the starter throughout the season). Bukich replaced Wade during Week Four against the Baltimore Colts after Wade completed just 5 of 21 passes. Bukich played the remainder of the game and completed 6 of 7 passes, including a pass to Ronnie Bull for a touchdown that was the deciding margin of victory.