Don't! You're just wasting paper, they're free and they get replaced for free. Leave the hobbit, most places I've worked at or know prior that work at won't take them unless someone says they lost a book.
The Gideon Bibles, found in very many hotel nightstands, remain property of Gideons International. GI supplies these bibles to hotels upon request. "Men who are members of our association, or Gideons, volunteer their time to place Bibles in hotels." These books have a six year lifespan. "Gideons will periodically check hotels to make sure that they are stocked and also check rooms (as they are available) to make sure the Bibles are in good condition."
Is it okay to take a Gideons Bible from a hotel room? "It is our intention that the Bibles remain in the rooms for use by the guest. However, if someone is in need of a Bible we are happy for them to take the one from the room."