Bassett (Basset) was born in Cecil County, MD., in April 1745. After his tavern-keeper father deserted his mother, he was reared by a relative, Peter Lawson, from whom he later inherited Bohemia Manor (MD.) estate. He read for the law at Philadelphia and in 1770 received a license to practice in Dover, DE. He prospered as a lawyer and planter, and eventually came to own not only Bohemia Manor, but homes in Dover and Wilmington as well.