Embroidery Library recommends Cut-Away for linen projects.

I recommend ussing the No show Polymesh type cut away, it is a super thin cut away that will give you excellent support and it does not shows thru the fabric.

Yes, a cutaway, definitely, but Adelmarie's suggestion of the no-show mesh is a good one. If the Bible (book itself) covers, the binding, is dark the regular cutaway would show behind the linen, I think. You might want to do a test swatch first, just to be sure how it all looks. Might even be best to use an iron-on, and leave the stabilizer behind the whole Bible cover, for added stiffness? I'm not sure what you mean by 'cover', like the book covers we used to use in school, a fitted one? I hope you get more answers, and possibly even clearer ones, hee hee hee. Best of luck, Marji