While Bocek was a student at the University of Wisconsin–Madison, he became a fairly prominent summer amateur and semipro player in baseball and softball.Chicago White Sox manager Lew Fonseca noticed him and arranged a tryout at Comiskey Park, during which Bocek hit several balls into the upper deck. He signed with the White Sox in the second half of 1933, becoming the fifth-youngest player in Major League Baseball that season, and then spent the first part of the 1934 season with the team as well. Subsequently, he played several years in the minor league systems of the St. Louis Cardinals and the New York Yankees.