Bican was a member of the Austrian "Wunderteam" of the 1930s and represented the nation at the 1934 FIFA World Cup, where they reached the semi-finals. He later switched allegiance to the Czechoslovakia national football team, but a clerical error related to his transfer of national team precluded him from playing in the 1938 FIFA World Cup. Bican was a tall and powerful player, with the technical ability to play with both feet, and had considerable pace. During his athletic prime, he was reportedly capable of running 100 metres in 10.8 seconds, which was not far off the leading sprinters of his time.