Bassett was born on March 18, 1764, at Eltham in New Kent County, the second of four sons and fifth of eight children of Burwell Bassett and Anna Maria Dandridge Bassett. Following a private education, he attended the College of William and Mary. At his father’s death he inherited the bulk of the large family estate, which consisted of about 6,000 acres of land in New Kent County and more than 1,000 acres in neighboring Hanover County. On January 10, 1788, Bassett married Elizabeth McCarty, of Westmoreland County, and following her death he married Philadelphia Ann Claiborne, who died in 1834. He had no children. Late in the 1790s Bassett purchased about 350 acres in James City County. He lived in Williamsburg from 1815 until 1837.
Like most public men of his time, Bassett held a commission in the county militia, but his service was largely perfunctory and social except during the British invasion of the Chesapeake in 1814, when he briefly took the field as lieutenant colonel of the 68th Virginia Militia Regiment. Bassett entered politics in 1787 and represented New Kent County in the House of Delegates for three years. His father was then representing the district comprising Charles City, James City, and New Kent counties in the Senate of Virginia, and following his death Bassett succeeded him in the seat and served from 1793 until 1805.
Bassett ran for the House of Representatives in 1795 but lost a close contest to John Clopton, who served in Congress for many years as a Jeffersonian Republican. In the 1800 presidential election Bassett supported Thomas Jefferson, and four years later he defeated incumbent Federalist congressman Thomas Griffin. Bassett sat in the House of Representatives from 1805 until 1813, when he lost a close election to Federalist, of Accomack County. In 1815 Bassett returned to Congress and served until he retired in March 1819. The voters of James City County then sent him to the House of Delegates, where he completed two consecutive one-year terms.
In 1821 he was elected to Congress again and remained until 1829. Early in that year he announced his second retirement, but friends persuaded him to seek one more term. In the meantime, however, many of the district’s leading Democrats had already pledged themselves to the candidacy of Richard Coke, who defeated Bassett in the April 1829 election. Shortly thereafter Bassett came in a poor last in a field of eight candidates for four seats in the Convention of 1829–1830. During his years in Congress he spoke occasionally, taking a special interest in reducing the naval establishment, but served only once on a standing committee, chairing the Committee on Claims during the first session of the 12th Congress. Bassett generally supported states’ rights positions advocated by his fellow Virginia Republicans, and during the 1820s he was sharply critical of the administration of John Quincy Adams.
Bassett served on the vestry of Bruton Parish while he resided in Williamsburg and was one of the most prominent and active lay leaders in the Episcopal Church in Virginia. He was a delegate to several state conventions, and in 1827 the convention named him a trustee of the Protestant Episcopal Theological Seminary in Alexandria. Bassett also sponsored a bill in the House of Representatives to incorporate Alexandria’s Episcopal Church, but in 1811 Presidentvetoed the bill, stating that it violated the First Amendment. Bassett also took an interest in and gave significant support and encouragement to the British educational reformer Joseph Lancaster, who stayed with Bassett in Virginia in 1819.
Bassett remained in many ways a man of the eighteenth century. A grandniece wrote many years later that he had been “perhaps the last man in Virginia who wore small clothes and powdered hair in a queue.” He could be condescending toward people he regarded as beneath him in social standing or too obtuse to share his opinions. In 1837 he sold his property in James City County and moved back to Eltham. Bassett died at Eltham on February 26, 1841, and was probably buried in the family cemetery there.