I can’t say this will definitely work because I don’t also have the problem of wearing down books outside of the bath but here are a few options:

• small tray table that sits horizontally from one edge of bath to the other edge (ideally one that’s solid, not with slats, to keep steam from hitting the book and you from dropping it in).
• hardback books (fall apart less easily in general, although unfortunately more expensive)
• gloves, if you’re prone to lots of hand sweat and that’s part of the problem
• protective cover (something like the You-Bumi), which I’ve heard relatively good things about but never tried myself. It allows you to turn pages and stuff all while keeping the book in a sort of bubble/raft-like container