As a student, he published illustrations and caricatures in the daily Politika and satirical magazine Ošišani jež.

In 1935, Bajić became one of Petar Dobrović's students, finishing his first year in Beta Vukanović's class at the Belgrade School of Arts in 1937.

[1] After Kingdom of Yugoslavia was invaded by the Axis powers of Germany, Italy, Hungary, and Bulgaria in 1941, Bajić joined the Partisans, Yugoslav anti-Nazi resistance movement.

Occupying forces captured him in Belgrade in October 1942 and imprisoned him in Banjica Concentration Camp.

In 1949, he graduated from the Academy of Arts in Belgrade in the class of Milo Milunović, Ivan Tabaković, and Nedeljko Gvozdenović.

His later work is characterised by numerous mosaics and fresco paintings (compositions in space), and particularly the memorial construction Partisan Necropolis in Resanovci (1971).