The account is estimated to be worth as much as £15m globally, with a UK spend of between £3m and £5m.
Creative for Bushmills was previously handled by Bartle Bogle Hegarty, on a project basis.
The Bushmills brand will be 400 years old in 2008. It is understood that BMB will create a multimarket brand campaign timed to coincide with the anniversary.
Diageo purchased Bushmills from Pernod Ricard in August 2005 for £200 million. Last week, Pernod Ricard launched a search for an agency to push its Jameson brand amid declining sales of whisky in the UK. The search is being brokered through Agency Assessments International.Both BMB and Diageo declined to comment.