She was bleeding Lookout, I think Bamber used her own blood to make it look as though she was holding the bible when she died however, I think he probably realised it looked too staged so he tried to cover up by opening the bible on a different page and placing it over the stain. The police probably closed it and didn't take note of which page it had been opened and assumed it must have been on the stained page. He then placed the gun on her and made sure her arm covered the finger marks. But put them together and bingo!
In that case there would be another stained page caused by the stain on the carpet after Bamber put it there. It's now recognised that the the bible is open at a different page in photographs of it on the carpet to the page where the alleged palm print was found.

If the police had found two different places where the bible has stained pages, they would have thought that they had Bamber bang to rights, since Sheila could not have been opening and closing the bible after she was dead. Instead they have prevented the bible from being examined and the issues clarified.
You seem to be saying that the bible has been opened at three different places in the relevant period.
1 The place where the alleged palm print is seen. Bamber in your scenario pressed Sheila's blood stained palm on it after she was dead.
2 The place where it was open when Bamber allegedly put it on the stain on the carpet after closing it and opening it at a different page.
3 The place it was open at when the police put it down again after closing it and opening it again.
The main objection is that there would be a stain from the carpet where (2) is concerned. There just can't have been, or the prosecution would have used it as proof of guilt.