Bušić was born in Gorica, a village in Bosnia and Herzegovina, Yugoslavia, and finished high school in Imotski. At the age of 20, he emigrated to Vienna. In Vienna, three years later, in 1969, he met the American student, Julienne Eden Schultz, who was studying German there and who soon thereafter became involved in the activities of the Croatian emigration. In coordination with Zvonko Bušić, she and a friend traveled to Zagreb and threw anti-Yugoslav leaflets on Republic Square, after which they were arrested and imprisoned. After release, Julienne returned to Vienna and in 1972, Julienne and Zvonko married in Frankfurt. Later they moved to the U.S. where he became a member and leader of the Croatian terrorist group called Croatian National Resistance.