Todorović had an extensive acting career, and has had roles in critically acclaimed Yugoslavian films such as Who's That Singing Over There (1980), The Marathon Family (1982), Balkan Express (1983), Balkanski Špijun (Balkan Spy, 1984), Time of the Gypsies (1988), and Underground (1995).

His father died when he was a child. Following secondary school, Bora completed army service, at which point he had no plans to pursue an acting career. However, his older sister Mira's passion for acting exposed him to the business and soon he became passionate about it as well. He enrolled in the Belgrade Drama Arts Academy, and eventually acted on stage at the Belgrade Drama Theatre. In 1957, Bora lived and acted in Zagreb, eventually returning to Belgrade in 1961. Between 1961 and 1983, Bora was a member of the "Atelje 212" theater in Belgrade, where he performed various roles. In October 2002, he appeared on the Zvezdara Theatre stage in Belgrade, in the play Larry Thompson.

In his last days, Bora Todorović alternated residence between Prague and Belgrade. He was married to Carolyn Kilkka, with whom he had two children, Dana and Tara. Bora also had a child from his previous marriage to Snežana Matić.

In November 2002, he received the Lifetime Achievement Award "Pavle Vujisić" for his roles in Yugoslav cinematography, and in December 2006, he received the Lifetime Achievement Award "Dobričin prsten" for his roles in Yugoslav theater.