|Born:||U?cie Biskupie, Poland (today Ustia, Ukraine)|
Born in Poland during the Russian and then German occupation of the country in World War II, his family was taken to a Nazi labor camp outside of Salzburg, Austria in 1942, where they would spend three years. He considered himself fortunate for having been taken a "labor" or "concentration" camp rather than an extermination camp, as was the fate for many other Polish families. At the camps, when they could find some free time, Bednarski recalls playing games with other camp detainees using makeshift soccer balls constructed from rolled-up socks.
Bednarski's football career began with the Texas Longhorns in 1956 after Head Coach Darrell Royal of the Washington Huskies was informed by his scout who had just returned from scouting Texas for the team about the "soccer-style" kicker named Bednarski. In contrast to the traditional football kick used at the time in which the kicker would approach the ball from directly behind and contact the ball with his foot, Bednarski approached the ball from roughly a 45-degree angle and made contact with the ball with the side of his foot, swinging his like in a "golf club"-like motion.