If I am going to recline and read, which I often do, I will take a hand towel and fold it and rest it on my chest. Then I rest my arms on the towel - if I feel anything damp I know I need to look.

Also depending on your bathroom, as in is there a huge amount of condensation then any sort of book will have issues. So good air flow can help. Keep in mind not all paper in all books were created equal - the paper in paperbacks is often thinner than hardcovers. I take this to mean there is a greater chance of them getting moisture due to how permeable the paper is. So I don't read paperbacks in the tub just to play it safe.