Joseph Bishop, Sr. was the son of Jeremiah Bishop III (aka Jeremiah Bishop, Jr.) and Mary (maiden name unknown). Joseph's parents were censused at Chemung, then part of Montgomery Co., New York, in 1790. The 1855 New York State Census shows his county of birth as Tioga. He is present in Scipio by 1795, when his parents and grandparents joined the newly organized First Baptist Church of Scipio at Stewart's Corners (now in the Town of Venice).

Joseph married (1st) Amanda Reynolds, daughter of Oliver Reynolds, Sr. and Lydia Reynolds, ca. 1811. They had three children: Almira A., Volney R., and Amory R. Bishop. Amanda died in 1818.

Joseph married (2nd) Mary "Polly" Beardsley, aka Mary "Polly" Bursley, on 18 November 1819 in Scipio. Joseph's family was censused in Scipio in 1820 and in the Town of Lansing, Tompkins Co., New York in 1830. Polly died in 1834, having borne seven children: Caroline Martha, Amanda, Harriet Ann, Edwin, Elizabeth Jane, Mary, and Augustus Bishop.

Joseph married (3rd), Mrs. Mary Hoyt, believed to have been Mary White, on 31 August 1836 at Farmerville (now called Interlaken), in the Town of Covert, Seneca Co., New York. Joseph and Mary took up residence in Scipio by 1837 when Joseph became very active in local politics with the Whig Party. In 1838 and 1839, Joseph was a member of the Whig Party Town Executive Committee for Scipio, and from 1839 to 1841 was one of two Coroners for Cayuga County, elected on the Whig ticket. Joseph served as President of the Scipio Clay Club in 1844 when Henry Clay was the Whig candidate for President. He was a Delegate from Scipio to the Whig Cayuga County Convention in 1845. Joseph was Inspector of Election for Scipio in 1847 and Town Supervisor in 1848 and 1849. In 1851, Joseph was Overseer of Highways for the Town.
The following year, he was a Delegate from Scipio to the Third Assembly District Convention at Moravia. Finally, Joseph served as an Assessor for Scipio in 1856. Joseph and Mary seem to have had only one child together, Joseph Bishop, Jr. The 1860 census shows Joseph as a Farmer in Scipio. Joseph and Mary appear to have resided on a farm about a half mile west of Scipio Center. He died in Scipio in 1865.