Bone was born in Stockton-on-Tees, the son of Christopher Bone, a tea merchant, and his wife Mary Elizabeth.
Bone was married twice: firstly in 1896 to Kate Hind, daughter of the Mayor of Stockton, with whom he had a son and two daughters before her death in 1914 and secondly in 1916 to Mabel Isabel Liddeard, who died in 1922.