Born in Mercer County, Pennsylvania, where his carpenter and bricklayer father, Hugh, had moved after service in the War of 1812, Bingham attended local public schools. After his mother's death in 1827, his father remarried. John moved west to Ohio to live with his merchant uncle, Thomas, after clashing with his new stepmother. The teenager apprenticed as a printer for two years, helping to publish the "Luminary", an anti-Masonic newspaper. He then returned to Pennsylvania to study at Mercer College, after which Bingham studied law at Franklin College in New Athens, Harrison County, Ohio. There, Bingham befriended former slave Titus Basfield, who became the first African American to graduate college in Ohio. They continued to correspond for many years.