If someone has one of the small "pocket benschers" that slide into his wallet, is it a problem for him to walk into the bathroom with his wallet in his pocket?
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When I was at KBY, I asked the campus Posek this question, and he said that it's OK, because the bentcher is protected by at least two layers of covering ("kli betoch kli"). He added that it may even be OK in a pants pocket without the wallet, since the fabric of the pocket and the fabric of the pants could constitute two layers.
You need two covers to be able to bring it into a bathroom. See Mishna Berura 40:4, Pri Megadim (Eshel Avraham 40:2), Maharam Shik (OC 94) and Da'at Torah (240) who assert that the binding is considered part of the book therefore two additional coverings are required.
But there are opinions that the cover of the bentscher is one cover (e.g., Kaf Ha-Chayyim 40:14). And according to the latter opinions, either the plastic cover (if it slips into one) or the pocket of your pants or the wallet is the second cover, so it is typically not an issue.
See here for a very complete answer with sources (mid page: Other Applications of "And Your Camp Shall be Holy": Bringing Tefillin and Sefarim into a Bathroom)
What is more problematic is to walk with a sefer into a bathroom - I have no good answer for this one except to leave it outside for a few minutes.