Bell was born in Falkirk in 1877, the son of the Rev. George Bell, a Congregational minister. The family moved to Hamilton and it was from Hamilton Academy that Bell went up to Glasgow University, taking a high place in the open Bursary Competition. In 1898 he graduated in Arts with First Class Honours in Mathematics and Natural Philosophy and was appointed William Ewing Fellow, part of whose duties was to help in the tutorial classes in the Department of Mathematics. In 1901 he was appointed by Professor Jack as the Junior Assistant in this department, later becoming a Lecturer, and he remained in Glasgow till his appointment to the Otago Chair.
In 1911 Bell was awarded the degree of D.Sc. at Glasgow for his work on the co-ordinate geometry of three dimensions. He later received three Honorary Degrees - LL.D. from Glasgow in 1932, Sc.D. from Cambridge in 1948 and LL.D. from Otago in 1962.
During his tenure of the Chair at Otago, Bell was prominently associated with the administrative work of the University, holding at various times the posts of Chairman of the Professorial Board and Dean of the Faculty of Arts and Science. He was a member of the Academic Board of the University of New Zealand and its representative on the University of New Zealand Senate from 1939 to 1946. After his retirement he was for a time a member of the University Grants Committee.
Bell will be remembered for his outstanding qualities as a lecturer and for his extremely successful textbook An Elementary Treatise on Co-ordinate Geometry of Three Dimensions. Former students recall with affection the time they spent in his lecture room. Dr J R Peddie writes: "I was in the Ordinary Mathematics Class in 1907 and am still able to recollect his brilliance as a teacher. He had an unruly class completely at his command and all he did was accomplished so quietly and effectively that he was able to give us, who were not likely to get beyond the ordinary stage, a real grasp of the elements of geometry and trigonometry". Bell's book on the geometry of three dimensions was published in 1910 and was an immediate success. It quickly became the standard textbook on the subject and was translated into several foreign languages, including Japanese and three of the Indian languages. His name became known throughout the mathematical world as the ablest expositor of his subject. Bell married, in 1902, Agnes Thomson and he is survived by his son, Mr G W J Bell of Dunedin, and by his daughter Mrs W N Searle of Lamlash.
He was elected a Fellow of the Society in 1916.