He was the son of the printer William Bradford (1722-1791) and was born in Philadelphia. He attended Princeton University where he formed a life-long friendship with a younger student James Madison before graduating in 1772. When he returned to Philadelphia he read law with Edward Shippen. His progress was delayed by the American Revolutionary War.
In 1776 when the Pennsylvania militia was called out, William volunteered as a private. Later that year the militia was organized into a flying camp with Daniel Roberdeau as the first Brigadier General in the states forces. General Roberdeau chose the young man as an aide, and later promoted him to brigade Major on his headquarter staff.
When his militia term expired he joined the Continental Army as a Captain and company commander in the 11th Pennsylvania commanded by Richard Hampton. By the end of the year, he saw action in the Battle of Trenton. While at Morristown, New Jersey he was named a deputy to the to the muster master-general on April 10, 1777, and he was promoted to Lieutenant Colonel. He resigned after two years due to ill health and returned home in early 1779.
Bradford joined the bar before the Pennsylvania Supreme Court in September 1779. He was named as the state's Attorney General in 1780, and served until 1791. In 1784 he married Susan Boudinot, the daughter of Elias Boudinot. On August 22, 1791 he was appointed to the Pennsylvania Supreme Court, and served for three years.
In 1793, Governor Thomas Mifflin asked his help to reduce the use of the death penalty. His report to legislature was in the form of an essay, "An Inquiry how far the Punishment of Death is Necessary in Pennsylvania". In the next reorganization of Pennsylvania's penal code, the use of capital punishment was substantially reduced. Other states followed the Pennsylvania example.
On January 8, 1794 George Washington named him Attorney General for the United States to replace Edmund Randolph. He died while in office in 1795, and is buried with his wife's family in the churchyard of St. Mary's Episcopal Church, Burlington, New Jersey.
Bradford County, Pennsylvania was named in his honor.