Bjegojević played with the Yugoslav national team in three major competitions. At the 1953 European Championship in Moscow where in nine games scored 34 points, and the team took the sixth place. It was a time when the Yugoslav basketball rules groundwork for later great success. Bjegojević at the 1954 FIBA World Championship in Rio de Janeiro, in five matches scored 46 points with an average of 9.2 points was the third scorer of the national team, which finished the competition in 11th place. In the only win of the tournament against Peru (86–84) recorded 20 points and free throws without a miss a shot (8-8). At the 1955 European Championship in Budapest, Yugoslavia was eighth, and Milan in nine games scored 49 points. In the triumph over Austria (68:61) he achieved a performance of 19 points.