Bogojević was a member of the Germany national basketball team that competed at the 1997 FIBA European Championship in Spain. Over eight tournament games, he averaged 6.6 points, 1.9 rebounds and 1.4 assists per game. He was a member of the team that competed at the 1999 FIBA European Championship in France. Over nine tournament games, he averaged 6.6 points, 2.6 rebounds and 5.2 assists per game.