Bishop was born in Sidney, New York, and attended Unadilla Academy, Cooperstown Seminary, and Walton Academy, all in New York, after which he taught school for several years. During the American Civil War, he enlisted as a private in Company C, Forty-third Regiment, New York Volunteer Infantry, in 1861, and was discharged in December 1862 because of a wound which necessitated the amputation of his right arm. He entered the University of Michigan, Ann Arbor, in September 1868 where he remained until December 1872. He studied law, was admitted to the bar in Ann Arbor in May 1875, and commenced practice in Ludington, Michigan. He was elected prosecuting attorney of Mason County in 1876, 1878, and 1884. He was a member of the Michigan State House of Representatives in 1882 and 1892.

Bishop was elected as a Republican from Michigan's 9th District to the United States House of Representatives for the Fifty-fourth and to the five succeeding Congresses, serving from March 4, 1895 to March 3, 1907. He was chairman of the U.S. House Committee on Ventilation and Acoustics in the Fifty-seventh through Fifty-ninth Congresses. He was an unsuccessful candidate for re-nomination in 1906 and resumed the practice of law in Ludington. He served as a member of the Michigan constitutional convention in 1907 and was appointed a member of the Spanish Treaty Claims Commission in December 1907 and served until the work of the commission was completed.

He moved to Hollister, California, in 1910 and engaged in fruit growing. He died at Pacific Grove, California, and is interred in the El Carmelo Cemetery there.