Bingham graduated from Milton Academy in 1960, where he was captain of the track team. He attended Yale University, where he participated on the freshman track and the varsity cross country teams. Bingham became involved in politics during his sophomore year, and was reportedly influenced by Allard Lowenstein. He was a member of the Yale Young Democrats and the Student Advisor Board, as well as the executive editor of the "Yale Daily News". In 1964, he graduated from Yale with honors, and spent two months in Mileston, Mississippi as a volunteer in the Freedom Summer civil rights project.