They're making quite an assumption that - that the Bible was put there after Sheila was shot.
We're not privy to all the information. Perhaps they had concluded that the blood on the bible did belong to Sheila.
If that is the case, then her limited movement after being shot makes it unlikely or dare I say it, impossible for her to have bled on the bible and then closed it before opening it again on the same page.
It might not be an assumption at all.