He held the positions of Professor of Pure and Applied Mathematics and Dean of the Faculty of Arts and Science, at the University of Otago in Dunedin, New Zealand.
In 1920 Bell was appointed Professor of Pure and Applied Mathematics at the University of Otago, Dunedin, New Zealand.
At Otago he joined another former pupil of Hamilton Academy and near contemporary, the physicist Robert Jack who had also gone on to graduate from Glasgow M.A.
Robert Jack had arrived at Otago six years before Bell, in 1914, taking up the appointment as Professor of Physics.
These two former Hamilton Academy boys from Scotland were to serve together on the faculty of the University of Otago (until Robert Jack’s retirement in 1947; Bell retiring a year later) in a building built by another former pupil of Hamilton Academy, Robert Forrest of McGill and Forrest, contractors, Dunedin.