Educated at Ayr Academy, Glasgow University and Balliol College, Oxford, Drummond Bone began his career as a professor of English, noted particularly for his work on Byron.
His first appointment was at the University of Warwick and in 1980 before he returned to Glasgow. After 20 years at the University of Glasgow, where latterly he was senior vice-principal, he became principal at Royal Holloway University of London, vice-chancellor at Liverpool and master of Balliol College, from which he retired in 2018.