Alojz Bajc took up competitive cycling at the age of 17 after having learned to ride at his mechanical workshop job. In less than a year, he was third in the junior Slovenian regional mountain championships, before winning the title in 1950. That year he also competed at the Yugoslavian championships, where he came second. He competed in the Tour of Yugoslavia every year from 1955 through 1961, as well as in numerous international races. Most notably, he represented his country in the road race at the 1960 Rome Olympics, where he placed 69th after a fall. He retired from active competition after 1961, but later worked as a coach throughout the 1960s.