Burd, the son of Colonel James Burd and Sarah (Shippen) Burd, was born February 5, 1749, in Philadelphia, Pennsylvania. He studied law with his uncle, Pennsylvania Chief Justice Edward Shippen, whose daughter Elizabeth he married on December 13, 1778. He was a member of the Berks County Bar, and had a law practice in Reading, Pennsylvania.
Upon the outbreak of the Revolution, Burd volunteered and eventually rose to major in Colonel Henry Haller's Pennsylvania Battalion of the Flying Camp. During the Battle of Long Island (1776), Burd was in command of an American pickets stationed at the Red Lion Inn, in the early morning hours of August 27, 1776 after an initial exchange of gunfire with British advance troops, he was taken prisoner along with 16 other Americans under his command. After his release, ill health prevented him from reentering military service, and he returned to his legal practice in Reading. He was appointed as Prothonotary of the Pennsylvania Supreme Court on September 1, 1778, and served with great distinction until his resignation December 29, 1805.