Stop in to almost any scuba diving shop, or large sporting goods store, big camera outlet, etc., etc. There are quite a few heavy-duty completely waterproof "dry bags" made just for this sort of use, most being guaranteed waterproof down to 10 meters (33 feet. ) In the camping stores you'll find waterproof 'map cases,' crystal clear vinyl and will withstand a bathtub session with no problems. None of them are particularly expensive, and all will keep an e-reader working in wet environments.
Stitchawl
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