Bučar was born in the small Upper Carniolan town of Bohinjska Bistrica in what was then the Kingdom of Serbs, Croats and Slovenes, now in Slovenia.

After the end of the war, Bučar was included in the Slovenian division of the Corps of National Defence (later renamed to OZNA), a Yugoslav military counter-intelligence service.

In 1956, he obtained his PhD at the University of Zagreb and moved to Belgrade, where he worked as a secretary in the Ministry of Foreign Commerce for one year.

In 1959, he travelled to the United States as an Eisenhower Exchange Fellow, studying for ten months at the University of Philadelphia.

During this period, Bučar started openly voicing his criticism to certain features of the Yugoslav Communist system, especially the excessive centralism and the not entirely successful economic integration of the different regions of Yugoslavia.

Unlike other prominent faculty, Bučar assumed a skeptical attitude towards the student movement in the years 1968–1972.

After 1968, he published numerous articles criticizing the establishment of large business systems in Yugoslavia, the frequent changes in the legal framework and the lack of clear responsibilities in decision-making processes.

During this period, Bučar insisted on providing a sound legal basis for Slovenia's independence from Yugoslavia, and rejected all voluntaristic political actions, gaining a label of legalist.