I flew two times with KL to BLL and got a gate position in both instances. When arriving you need to go left to the transfer door, not right to baggage claim where all people go (then you would need to re-enter the gate area through the main security.
From the discussion on the BA board, it would seem that there is one caveat, which is that the transfer door might be closed if there is a non-EUR flight (such as a TK flight) arriving around the same time, in which case you would have to go via landside. The general consensus on the BA board seems to be that, even if that is the case, the detour via landside should be fairly quick but you might have to jump the queue if security is busy at that particular point in time..