After graduation, he joined the United States Naval Reserve serving from 1959 to 1963 in the grades of ensign to lieutenant.
On leaving active service, Dudley became a history teacher at Poly Prep Country Day School in Brooklyn, New York, while also earning his Master of Arts degree in history at Columbia University, between 1963 and 1966.
Completing his master's degree in 1966 with a thesis on "Pedro de Angelis, 1784-1859: journalist, historian and propagandist", he went on to work on his doctorate, which he completed in 1972 with a dissertation on "Reform and radicalism in the Brazilian Army, 1870-1889".
Dudley began work on the series "Naval Documents of the American Revolution," beginning with volume 8, under its editor Dr. William J. Morgan.
In 1995, the Navy Department selected Dudley for a Senior Executive Service appointment to succeed Dr. Dean C. Allard as Director of Naval History.