If she had the wherewithal to walk around the bed and back to the door there was no reason for her not to carry her bible. You don't know what she was concerned with in those last moments and what took precedence.
I know it's splitting hairs but I would use the term stagger not walk to describe any movement from June.
It seems reasonable to assume that a mortally wounded person shot several times in the face and limbs would have been preoccupied with their pain/wounds at that stage, not the bible.
And then she conveniently dropped this bible exactly beside where Sheila was later found laying after she had taken her shower to wash the blood, residue and sugar off her in order to frame Jeremy? Good grief!
No, It was arrogant stupidity from Jeremy to plant the bible. Things went broadly according to his plan that night but he must have turned white when he realised a second shot was needed to finish Sheila. The bible was a convenient prop to shore up the deranged nature of her crime.