Born in 1837 in Dansville, New York, Bradley was still living in that state when he joined the Navy. He served during the Civil War as a landsman on the . At the Battle of Forts Jackson and St. Philip near New Orleans on April 24, 1862, "Varuna" was rammed twice by the Confederate steamer (formerly known as the "Charles Morgan") and eventually sunk. Bradley was stationed at the ship's wheel and showed "the greatest courage" throughout the close-range fight. For this action, he was awarded the Medal of Honor a year later, on April 3, 1863.