Radonjich was born in 1943 in Užice. Bosko's father Dragomir was a teacher, who was captured and executed during World War II by the Josip Broz Tito's Partisans for his belonging to the Chetniks led by general Draža Mihailović. Stigmatized as a son of a royalist Chetnik soldier, Radonjich grew up in communist Yugoslavia under Tito.