After consideration, other posters and Julie may have been correct that Bamber shot the twins first.
This would have just been one shot each into each twin. Shooting them 8 times first then going downstairs to reload would have been madness.
It is doubtful that June would have been able to walk across the bedroom and back again if she received all 7 shots straight away. The 2002 appeal said two of the head shots would have caused death very quickly. It is likely she received five intial shots.
If Bamber believed June was worthy of 7 shots, then Neville was worthy of at least as many. However the rifle only held a maximum of 11 bullets.
I suspect Bamber correctly believed 4/5 accurate head shots each were sufficient for Neville and June. Which is why he could afford two early shots into the twins.
It is quite possible that -
Bamber shot each twin once. This would be quick and would prevent any possible noise from them. It would also be unlikely these two shots would wake anyone else inside WHF (2 shots).
Bamber then walked straight across the landing and fired five shots into June. And four shots into Neville (9 shots).
Rifle now empty.
After the kitchen fight, the rifle was fully reloaded and fired into Nevile (4 shots).
Bamber returned upstairs and fired more shots into the twins to make it seem like an 'out of control' killing (6 shots).
There was now one bullet left for Sheila who was the only person still alive. Either still asleep or putting up no resistance if awake. Bamber attempted to kill her with the one remaining bullet (1 shot).
Rifle now empty.
Before leaving WHF, Bamber realised Sheila may not be dead. And already knew June had moved. He couldn't burn everyone's back like he had done with Neville. So loaded three more bullets into the rifle
A fatal shot fired into Sheila (1 shot)
Fatal shots fired into June (2 shots).
Rifle now empty and on top of Sheila.