In 1887, he was admitted to the Fountain County bar, but during the course of his "tireless study of law", he had severely damaged his eyesight.
Bingham served in the administrations of Governors Frank Hanly (a Republican) and Thomas R. Marshall (a Democrat).
Edward M. White, a judge from Muncie, served as Assistant Attorney General under Bingham (the two would later practice law together).
Bingham was involved as an attorney in two test cases originating from Ohio that led the U.S. Supreme Court to affirm the constitutionality of the Eighteenth and Nineteenth Amendments, enacting nationwide Prohibition and granting women the right to vote respectively.
[3] In 1908, Bingham wrote a letter to U.S. President Theodore Roosevelt encouraging him to seek a third term instead of allowing William Taft to be the Republican nominee in the upcoming election.
One of their sons, Remster A. Bingham, was a national judge advocate of the American Legion and a member of the state board of law examiners.
Another son, Charles Bingham, served in the First World War and died young of an illness caused by his service.