Bingham earned an associates degree at the University of Alabama in 1942. He served in the U.S. Army during World War II and graduated from Harvard Law School in 1948. He then followed his father into the firm then known as Martin Turner & McWhorter. A year later he helped organized the Harbert Construction Corp., which he served as a director and secretary.
In 1953 Bingham was made a partner in what was, by then, Martin & Blakey. In 1959 the firm became Martin, Vogtle, Balch & Bingham. During his career he specialized in condemnations, mortgage indenture, mortgage-backed securities and preferred stock sales. He participated in each of Alabama Power Company's plant certifications from 1950 to 1991.
Bingham retired from the Army Reserve in 1980 and from his law practice in 1991. In addition to his practice, he was a trustee of the Legal Aid Society, chairman of the board of management for the Downtown YMCA, and president of the APCO Employees Credit Union. He was also a former vestryman and warden at The Episcopal Cathedral Church of the Advent.
Bingham died in 2009. He was survived by his wife, Jean, and their children and grandchildren.
- Jarvis, Crystal (December 8, 2009) "Balch & Bingham namesake Jack Bingham dies." Birmingham Business Journal