Bapst is a surname. Notable people with the surname include:
Germain Bapst (1853–1921), French jeweler and historian Jacques-Evrard Bapst (1771–1842), French jeweler Jeanine Bapst (born 1968), Swiss ski mountaineer John Bapst (1815–1887), Swiss Jesuit missionary and educator Bapst Library, a Boston College library
See also Pabst