The obvious thing is for BMI to become a BA franchise with BA reallocating domestic slots to European services, "babysitting" them for use on long haul in the longer term.
They won't be a franchise as they'll be owned by BA, in the same way BA CityFlyer are owned by BA. There's good operational flexibility in mainline operating domestics as they can balance a load of A319s-A321s against demand, there would be less of that with only BMI operating them.
There is no business case for the BMI brand surviving, none at all. LHR-BHD / DUB will have the option to be served via Aer Lingus' existing DUB and BFS services, freeing up slots for long haul, as the model states. BA could not make Northern Ireland pay and if anything it's less likely to work now.
As for Virgin, they're no longer serious players, and they certainly do not have the skill set in place to save BMI, not in a million years.