Bach began his basketball career in New York City in the early 1940's playing on two New York City Catholic High School championship teams. As a freshman at Fordham, he was a regular on the school's great 1942-43 squad. His career with the Rams, however, was interrupted by years at the University of Rochester, Brown University, and the U.S. Navy ROTC program. He was commissioned as an ensign in the Navy and served until late 1947, at which point he returned to Fordham, earned a B.S. in economics and garnered team MVP honors for the 1947-1948 season.

In 1950, he took the head coaching position at Fordham and, over the next 18 season, compiled a 263-193 record with five NIT appearances and NCAA appearances in 1953 and 1954. He served as assistant to the athletic director for four years and as athletic director for his final eight years before leaving for Penn State after the 1967-1968 season.

He entered pro ranks after a decade-long term as head coach of the Penn State Nittany Lions, where he registered a 122-121 record. He then moved on to the Golden State Warriors where he logged a 136-188 mark in three-plus seasons as an assistant in Oakland before the Warriors head coach Al Attles stepped down late in the 1982-83 season. Bach assumed interim responsibilities for four games, before being named Warriors' head coach for 1983-84. He went 89-157 as the Warriors head man over three seasons, before leaving to join Doug Collins in Chicago.

In Chicago, he worked under both Collins and Phil Jackson. The Bulls accumulated a 432-224 (.659) record during Bach's tenure, notching 50 or more win six times. He also has three NBA Championship rings, won with the Bulls in 1991, '92, and '93.

Bach then joined the Hornets in 1994. The 1994-95 Hornets team yielded 97.3 points per game, almost 10 points better than that team had yielded before Bach arrived in Charlotte. Two years later, he reunited with Doug Collins, working with the Detroit Pistons staff for the 1996-1997 season. He most recently worked as Washington Wizards assistant coach.