Bistrić has not only acted as a chess player but also as a chess organizer. His commitment to chess is reflected in the fact that he brought numerous chess events to Sarajevo in the 1980s. Between 1986 and 1990, he was the director of the Defence of Peace tournament in Sarajevo, one of the world’s strongest chess tournaments at that time.
He was also engaged in the work of the Chess Federation of Bosnia and Herzegovina, serving as its president between 1993 and 1994. During his presidency, the Chess Federation of Bosnia and Herzegovina became a member of FIDE. He also was a member of FIDE from 1993 to 1994.