In 1819, he married Nancy Opie Ball (1802-1877), daughter of a wealthy Virginia colonel. The couple had four children, Emily Caroline (1820-1891), Lucius Lee (1821-1898), Woodville (1823-1840) and Frederick Jr. (1826-1862). In 1824, Bates became the second governor of Missouri, and died in office in August 1825, in Chesterfield, Missouri, due to a short illness thought to be pneumonia. Bates was buried at the family cemetery on the Thornhill estate near St. Louis.
During his time in Missouri, Bates acquired nearly 1000 acres (4 km²) of land which became the estate known as Thornhill. On the estate was built a reserved Federal style home with high ceilings for summer ventilation, fine woodwork and a sophisticated floor plan; all this would have been familiar to Bates from his childhood home, Belmont, in Goochland County, Virginia. The Thornhill estate still exists today and can be viewed by the public. It is located in Faust County Park in Chesterfield, Missouri.