Well, the problem is that there are simply not many airlines around that could offer flights. Who is left? Loganair, Eastern Airways. That's it. They are small operators with mostly 30-50 seat equipment. Maybe Jet2 for LBA as they served the route in the past (although domestic flying is not really part of their business) and BACF for LCY.
easyjet serves GLA, EDI, NCL, BHX, BRS, IOM, LPL, STN, LGW, LTN, MAN from BFS. Short of moving their base to BHD, why should they offer those destinations from BHD instead of ramping up frequencies at BFS? The fact that Loganair has taken up INV and ABZ from BE, but not their core markets GLA and EDI shows that there is little point for them to serve destinations offered by a LCC from BFS.