Bayard was a member of a distinguished family. He was directly descended from the French hero the Seigneur de Bayard and from Ann Bayard, a sister of the Dutch governor of New Amsterdam (New York) Peter Stuyvesant. His great-grandfather Richard Bassett (1745–1815) was governor of Delaware; his grandfather James Asheton Bayard (1767–1815) was a prominent Federalist congressman from Delaware and one of the U.S. commissioners who negotiated the Treaty of Ghent with Great Britain that ended the War of 1812; his uncle Richard Henry Bayard (1796–1868) was chief justice of Delaware; and his father, James Asheton Bayard (1799–1880), was a well-known constitutional lawyer. All of the foregoing represented Delaware in the U.S. Senate.

Bayard's formal education was limited to a few years in an academy in Flushing, N.Y. He did not attend college but in 1848 began the study of law in the office of his father and was admitted to the bar in 1851. He practiced chiefly in Wilmington and served for one year (1853–54) as U.S. attorney for Delaware, an office that his father had held some years earlier. During the sectional crisis of 1860–61 he was instrumental in keeping Delaware in the Union. He served in the U.S. Senate (1869–85), succeeding his father, and was secretary of state in the first administration of President Grover Cleveland (1885–89).

In 1893 Bayard was appointed ambassador to Great Britain, the first U.S. representative to Great Britain to hold that rank. As a champion of arbitration, he was critical of the aggressive position taken by Cleveland in the dispute with Great Britain over the Venezuelan boundary (1895). His critics thought him too pro-British, and he was censured by the U.S. House of Representatives.

Because of failing health, Bayard left London in 1897. His son, Thomas Francis Bayard (1868–1942), represented Delaware in the U.S. Senate in the 1920s.