I'd say it's extremely unlikely for there to be enough room for BE to serve the CIs, certainly not profitably.
It's worth noting that Loganair currently serve ABZ, INV and IOM from BHX. If they were to potentially add GLA/EDI to that list, and taking into consideration the new tripartite partnership that they've just inked between themselves, GR & SI, I think they'll have the BHX to CIs market pretty much covered.
For those travellers who fly between Scotland and the CIs, I'd guess that they'll more than likely make use of the existing option of connecting via SOU, or the direct easyJet service to JER from GLA.
As for BHD, Emerald Airlines will almost certainly be considering BHX as a key route in the future once they've obtained their UK AOC and they'll simply take over from BA Cityflyer who only stepped-in as a consequence of Stobart Air's demise.