There is another possibility which deserves consideration. It is consistent with Mike Tesko's opinion that Sheila was shot a second time at some time later than 09:00am.
If the stain on the carpet which the bible is partly covering was made by Sheila's blood it would, on this view, have been still wet when the police for some reason put the bible on it.
The campaign team apparently have proof that the photographs showing Sheila with the rifle on her were taken at around 10:20. If you relate this to the opinion given by professors Meloni and Cavalli that Sheila could not have been dead for more than than two hours when the well known police photograph showing wet blood was taken, the implication is that she could not have died at any time earlier than 08:20.

You have to consider the possibility that there WAS a stain on the page of the bible resting on the stain on the carpet, if it is Sheila's blood. That would explain why the defence were not allowed to have it examined.
It might be suggested that the police could have used such a stain, caused by themselves, to frame Bamber, but Bamber was not a suspect at that stage.
If the police had, weeks later, tried to use such a stain as evidence against Bamber that would beg the question as to why they didn't figure out he was the culprit straight off. So, if there was a stain at the page in question, the chance to use it as false evidence had already passed.
I admit I favour the view that the stain on the carpet was from June's blood and that it was dry.