Bullard was born in Columbus, Georgia the seventh of 10 children born to William (Octave) Bullard, a black man from Martinique, and Josephine ("Yokalee") Thomas, an Indigenous Creek woman. His father's ancestors had been enslaved in Haiti by a French slave master who later fled during the Haitian Revolution. Following the revolution, Bullard's ancestors left the Caribbean for the United States and took refuge with the Native Americans of the Creek tribe. Bullard attended the 28th Street (Grammer) School in Columbus from 1901 to 1906 completing the 5th Grade.