Bishop was born September 5, 1847 in Seekonk, Massachusetts, today the village of Rumford in East Providence, Rhode Island. He was the sixth of seven children of James Madison Bishop (1812–1864), a farmer, and Elzada Balcom Bishop (1808–1892), a homemaker. His ancestors were early New England settlers, arriving in Salem, Massachusetts from England in 1639. Bridget Bishop, his great grandmother via marriage, was the first woman executed during the Salem Witch Trials of the 1690s. Shortly after Bridget's death on June 10, 1692, the family escaped to Rehoboth, Massachusetts where many later generations of Bishops lived and worked. Joseph's great grandfather, Phanuel Bishop, a wealthy innkeeper in Rehoboth, led a company of Minutemen that marched on the alarm of the "shot heard ‘round the world" at the Old North Bridge in Concord, Massachusetts. Phanuel Bishop was a member of the United States Congress from Massachusetts (1799–1807) and a delegate to the Massachusetts Constitutional Convention of 1778 in Boston.