Bleier graduated from Xavier High School in Appleton, Wisconsin in 1964; while in high school, Bleier starred in football and basketball. In football, he was a three time All-State pick as running back, and also won All-Conference honors at both linebacker and defensive back.
He graduated from University of Notre Dame in 1968 with a degree in business management, in addition to starring in football.
After his rookie season, Bleier was drafted into the army, and fought in the Vietnam War. On August 20, 1969, Bleier's platoon was ambushed and Bleier was wounded in his left thigh. While he was down, a grenade sent many pieces of shrapnel into his right leg. Bleier's struggle to recover from his injuries was dramatized in the 1980 film Fighting Back starring Robert Urich as Bleier and Art Carney as Art Rooney.
Bleier would play sparingly from 1971 to 1973 as upon his return he couldn't walk without being in pain, and he weighed only 180 pounds (82 kg). Chuck Noll, the Steelers coach, waived him on two occasions, but Bleier would always regain a spot on the roster. An offseason training regimen brought Bleier back to 212 pounds in the summer of 1974. From that point in time, he would be in the Steelers' starting lineup.
In addition to being a great lead blocker, Bleier was the second of the Steelers' rushing weapons, (Franco Harris was the primary back,) but was effective nonetheless at both blocking and rushing. In 1976, both Harris and Bleier rushed for over 1,000 yards.
Bleier played in all four Steeler Super Bowl victories, and caught the touchdown pass from Terry Bradshaw that gave Pittsburgh a lead it would never surrender in Super Bowl XIII.