Grandfather William Bassett married a daughter of Lewis Burwell II, became the first member of the family to win election to the House of Burgessses (in 1693) and was selected for the Governor's Council in 1707.

In 1753, Burwell Bassett married Ann Kidley Chamberlayne, but she died the following year and their daughter never reached adulthood.

On May 7, 1757, Bassett remarried, this time to Anna Maria Dandridge, whose father was a member of the House of Burgesses.

[1] New Kent County voters first elected Bassett as one of their representatives in the House of Burgesses in 1762, following the death of Gil Armistead.

[7] Following his death, his son Burwell Bassett Jr. won election to the Virginia Senate seat his father had held for so long.