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.

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.

In October 1795 he was the Federalist candidate for governor, defeating Dr. Archibald Alexander, a retired army surgeon.

Bedford died at New Castle and is buried there in the Immanuel Episcopal Church Cemetery.