Depends how you view things, 'Biz jets' or 'business aircraft' come under two main groups, a 'corporate aircraft' owned either by an individual or a company for private use only... or a fractional ownership/charter operation.
Aberdeen has had in the past an 'N' registered Conquest turbo prop based here and also a Golden Eagle, both privately owned and operated. The well known chap who owned the conquest has moved to sunnier climes and the Golden Eagle 'bought the farm' at Humberside a few years ago.
The majority of Biz jet movements in Aberdeen would appear to be from the likes of Netjets who dont need to base an aircraft up here but they do have crews using the North East as a gateway.
It has always surprised me that so far none of the wealthy oil support companies have felt the need to own and operate a corporate aircraft up here, especially considering the crap airline route network here and the increasing hassle in airports with security etc.
However, it is being looked at!