KLM has 3 main waves of European arrivals (2 morning, 1 evening), as well as a more spread out fourth wave in the afternoon.
The most popular wave for UK/Ireland flights arriving into AMS is the third wave, with 17 out of 18 airports (including BHD) operating during this period. The first wave includes 14 airports, and the second wave includes 15 airports.
The early morning wave of KLM European flights depart the UK/Ireland between 05:55-06:30, and arrive in Amsterdam between 08:10-09:00. A 05:55 departure from BFS (which is the same as from DUB) would mean the aircraft would arrive in AMS at approximately 08:35, right in the middle of the UK/Ireland early morning arrivals. It would also require an overnight stop, which KLM already do at 14 UK/Ireland airports.
Based on KLM's current BHD schedule and KLM's other UK/Ireland operations, then this would be the likely schedule for double daily flights to BFS.
BFS-AMS: 05:55-08:35
AMS-BFS: 16:05-16:45
BFS-AMS: 17:50-19:15
AMS-BFS: 21:35-22:15
This schedule allows for BFS passengers to arrive in AMS in time for two waves of European flights, plus the vast majority of long haul departures. Comparatively, KLM's current BHD schedule allows for only one wave of European departures, and a select few long haul destinations to Asia and South America.
However, I would not be surprised if KLM were to add an additional third daily flight from BFS. Only 3 out of KLM's 18 UK/Ireland airports do not have at least three daily departures (BHD, INV, SOU), so expansion from BFS would likely mean three daily flights.
If KLM were to add a third daily flight, the likely flight times would be as follows;
AMS-BFS: 07:45-08:25
BFS-AMS: 08:55-11:35
Thus would mean BFS passengers would be able to arrive in AMS in time for three waves of European flights, plus all long haul departures.