I very much doubt that KLM would fly to BFS. For a legacy carrier such a KLM rock bottom fees is not always top of the list. Even if BFS were cheaper I'm sure BHD wouldn't be far off the mark.
It's all to do with airport experience awell. BHD as we know has most the boxes ticked nice modern airport, good location, good business lounges etc and not the big orange giant
And I'm pretty sure hour restrictions won't affect them