Obviously, reading the Kindle in the bath does not sound like a good idea. Even if you're not worried about splashing it or dropping it in the water, the steam that rises from the water and condenses on whatever's above it (and often makes your book a bit wrinkled) should be a concern.
But, there's a pretty easy way to deal with it and it worked pretty well when I tried it yesterday. Just get a medium-sized Ziploc bag, put the Kindle inside, and seal the bag. It keeps all the moisture off and the plastic adds hardly any impediment to reading the screen if you hold the plastic taut while reading. It's still easy to hold and push the buttons for page turning.
I'm not sure if it'd survive being dropped in the bath, but in theory it should (since the Ziploc seal is
good enough for keeping marinades contained).