Bateson was born in Liverpool, Lancashire. He was the son of William Gandy Bateson and Agnes Dingwall Bateson (née Blaikie). He was the older brother of
Sir Alexander Dingwall Bateson. Bateson entered
Rugby School on 2 May 1869. Bateson was married to Susan Clara Lemonius on 19 October 1881, at All Hallows Church. Susan's brother, Gerard MacLean Lemonius C.B.E. was also another Old Rugbeian who went on to play for
Clifton R.F.C. ==Oxford University==