The BA franchise did fly both BRS-EDI and BRS-GLA 5 x daily on the two routes for several years using E145s for much of the time against easyJet's 3 x daily to both Scottish cities.
It all ended in 2007 when Flybe bought BAConnect and closed the 5-aircraft (all E145) BRS-base.
BACon were also flying daily to FRA, MUC, DUS, ZRH, MXP and CDG (the latter 5 x daily but no easyJet on that route then), with FRA the longest served route at nearly ten years of operation.
Summer 13 timetable shows easyJet at 4 x daily some days on both EDI and GLA so, as others have pointed out, that looks a non-starter for bmi regional though there are several hours from mid morning till early afternoon with no coverage at present.
It looks as though regional might be looking at replicating some of the BACon European network.
I take CabinCrewe's point about fuel consumption - it's a far bigger cost item now than it was in BACon/BACx's time from BRS - and as yet no interlining/code sharing has been announced so far I know.
However, I am not as pessimistic about the initiative as CabinCrewe appears to be.
BRS is the sort of airport that bmi regional would hope to make a mark at with no competition on key routes such as FRA. If it can't make a fist of things at BRS where will it go? To larger airports with more competition?