Bannister attended John F. Kennedy High School in La Palma, California and then played college baseball at Arizona State University.

Although versatile (he played every position but pitcher and catcher) he never lived up to his college billing and was rarely a regular.

[4] He opened the 1975 season as the Phillies' starting center fielder until the arrival of Garry Maddox from the San Francisco Giants on May 4.

He was traded with Dick Ruthven and Roy Thomas to the Chicago White Sox for Jim Kaat and Mike Buskey on December 10, 1975.

In 12 major league seasons he played in 972 games and recorded 3,007 at bats, 430 runs, 811 hits, 143 doubles, 28 triples, 19 home runs, 288 RBI, 108 stolen bases, 292 walks, with a .270 batting average, .334 on-base percentage and a .355 slugging percentage.