Bassett was born in Cecil County, Maryland, to Michael and Judith Bassett.
His father, however, abandoned his family, and a relative, Peter Lawson,
adopted him. Richard Bassett owned large tracts of land in Kent
County, Delaware, and Cecil County, Maryland, as well as a house in
Wilmington. Bassett was a delegate to Delaware's 1776 and 1791
Constitutional Conventions. He served in the House of Assembly in
the 1780s. Bassett supported the drive for the U.S. Constitution,
serving as a delegate to the Annapolis Convention in 1786, the
Constitutional Convention in Philadelphia in 1787, and Delaware's
ratifying convention in December 1787. With George
Read, he was one of Delaware's first United States senators.
Bassett was governor of Delaware from 1799 to 1801. He married
twice, first to Ann Ennals and then to Miss Bruff. Bassett was the
great grandfather of suffragist Florence