The motivation for the present work is provided by Giuli and Salbany's work on the categoryBTOP0ofT0?bitopological spaces wherein they identified a cogenerator Q and a closure operator and used these to obtain, among other things, two interesting epireflective subcategories ofBTOP0consisting of objects which they referred to as 'absolutely 2T0-closed' and 'bisober' respectively. Moreover, the first such subcategory was also shown by them to be the epireflective hull of Q inBTOP0. We show here that almost a perfectly analogous programme can be carried out within the categoryBFTS0of 2T0-fuzzy bitopological spaces after identifying a key cogenerator inBFTS0.