Bedford was born on a farm in New Castle Hundred, near the town of New Castle, son of William and Catherine Jacquett Bedford. William Bedford was the grandson of another William Bedford who came to Delaware from Virginia around 1680, and who himself was the grandson of an English immigrant to Jamestown, Virginia, in 1621. Gunning Bedford was educated at the Academy of Pennsylvania and married Mary Read, the sister of George Read in 1769. They had no children. They lived at 6 The Strand in New Castle and were members of Immanuel Episcopal Church. He began his career as a merchant at New Castle, but later studied law, and was admitted to the Delaware Bar in 1779.
Political career
Bedford was elected to four terms in the House of Assembly beginning with the 1783–84 session and serving through the 1786–87 session. He was elected a delegate to the U.S. Congress under the Articles of Confederation in 1786–87, but resigned shortly afterwards on January 15, 1787. He then was elected to a term on the Legislative Council beginning with the 1788–89 session. In October 1795 he was the Federalist candidate for governor, defeating Dr. Archibald Alexander, a retired army surgeon. He served as governor from January 19, 1796, until his death on September 30, 1797.
Elections were held October 1, and members of the General Assembly took office on October 20 or the following weekday. State legislative councilors had a three-year term, and state assemblymen had a one-year term.
Beginning in 1792 elections were held on the first Tuesday of October, and members of the General Assembly took office the first Tuesday of January. Also in 1792 the State Legislative Council was renamed the State Senate, and the State House of Assembly became the State House of Representatives. The State President became the governor and was popularly elected. He takes office the third Tuesday in January and had a three-year term.