Bew was born in Belfast. He attended Campbell College, Belfast, as a youth, before studying for his BA and PhD at Pembroke College, Cambridge. His first book, Land and the National Question in Ireland, 1858–82 was a revisionist study that challenged nationalist historiography by examining not only the clash between landowners and tenants, but the conflict between large and small tenants as well. His third book, a short study of Charles Stewart Parnell, challenged some of the arguments of the award-winning biography of Parnell by F. S. L. Lyons, though Lyons, one of the "doyens" of modern Irish history, acknowledged the young historian's arguments by stating that "Nothing Dr Bew writes is without interest." Bew's central thesis is that Parnell was a fundamentally conservative figure whose ultimate aim was to secure a continuing position of leadership for the Protestant gentry in a Home Rule Ireland.
In 2007, Oxford University Press published Bew's Ireland: The Politics of Enmity 1789–2006, which forms part of the Oxford History of Modern Europe series. The book has received positive reviews.
Bew also acted as a historical advisor to the Bloody Sunday Inquiry between 1998 and 2001.
Bew was also involved in the project by Boston College to record interviews by former participants in the Irish "Troubles", including former republican and loyalist paramilitaries. In 2014, Gerry Adams criticised Bew's handling of the Boston College project, as well as the journalist Ed Moloney and the former IRA volunteer Anthony McIntyre. Adams claimed Bew had deliberately chosen Moloney and McIntyre because they were unsympathetic to Adams. Bew expressed regret over the closure of the project,and stated further oral history projects of the Troubles were now "under a cloud".