He didn't, how did he know she wouldn't of picked up another one of the many guns in the house? Call the police? Incapacitate him? Wound him somehow? How did he know they'd all be asleep? He apparently knew there had been a heated discussion that night so casually pops round breaks in through a window when he may have been greeted with any one of them? How would he explain that away?
Sheila call the police or fire a gun while Bamber is trying to commit a 2am massacre ?
Bamber had a strategy which I've just briefly put on another thread. It all seems straight forward to me.
He will be aware of unlikely difficulties but was prepared to take the small risks for the huge rewards.
The only difficulty he ended up facing was Nevill waking seconds before fatal shots.