Bell was born in Wichita, Kansas, where he played multiple sports at Bishop Carroll Catholic High School from 1971 to 1975.
He attended Colorado State University, where he played for the Colorado State Rams football from 1975 to 1978. He was recognized as a consensus first-team All-American as a senior in 1978. His twin brother Mark Bell also played for Colorado State.
The Kansas City Chiefs chose Bell in the first round (second overall pick) in the 1979 NFL Draft, and he played for the Chiefs from 1979 to 1991, playing for four head coaches. During his twelve NFL seasons, he played in 135 games and started 100 of them, while compiling forty quarterback sacks and ten recovered fumbles.