It looks like it says "by her right side" to me. That's interesting.
Could it also say "by her right shoulder"?
no...his odd writing style can be worked out and it says side.
The issue of the bed...does he mean "on" it or "on" the floor.
If Sheila was on the bed then in such a position he would need to say whether the rifle was on her left side or right side...to distinguish it and make things clear. It would be unsatisfactory to leave it as plain "by her side".
However if Sheila was on the floor as in the released photographs then he would not need to distinguish with by her right side as the bed automatically ruled out the rifle being on her left side. In such a situation he would not need to clarify anything other than the rifle was "by her side" as this could automatically be deduced by default.
With such an argument it adds a little weight to her being on the bed and supports that interpretation better than an on the floor interpretation.