Bodega was born in Guayaquil, Ecuador on February 9th, 1869, the only child of Ernesto Bodega, a Chilean naval architect, and his Ecuadorian wife Barbara Flores. When Francisco was four years old, his mother died of an undiagnosed illness which historians have speculated was likely to be some form of cancer; and he and his father moved to Valparaíso, Chile. Growing up among sailors of the Chilean navy, he became intrigued by the military lifestyle, and at 17, he enlisted in the joint Army-Navy expedition to Antarctica, to defend the Chilean settlements on the continent.