I'm not exactly sure how a standard hotel room contract works, but assuming I am renting the room and have ownership-like responsibilities for everything in it, is it a problem if there is a Gideon's bible in the room? What about other non-Jewish religious items, like a picture/statue of Buddah?
In regards to whether you have ownwership with a rental.
This was in response to whether one can carry on Shabbat from ones room to another's room without an Eiruv Chatzeros.
Paintings/Pictures of Avodah Zara (here a cross is referenced). Source here
In regards to the objects of Buddhism, they are definitely considered avodah zara.
However, there is a discussion of whether idolatrous images as art are considered avodah zara. Look Here
However the above only applies to being lenient in profiting from a sale and ownership(cf. Look Here above). So whether its a problem to own them at all is debatable.
These are all generalities though, any action taken should be consulted with a qualified Orthodox Rabbi.
It's all hotel property (or it may even belong to some religious group, not the hotel), not yours. So it's not your problem. The best thing to do is just ignore it.
Here's a quick test: if you were out at a conference and lightning struck the hotel room and burned it down, would the hotel expect you to pay for a new bible? Of course not! (If you damaged their property, that's a different story.) Not your responsibility, property-wise? Then not your responsibility, religion-wise.
The Talmud talks about owning Chametz on Passover; there were Jews who had to store food for the Persian army in their houses. The arrangement was that the Jews had financial responsibility over it, i.e. if the house burned down due to lightning strike, the Jew would be expected to replace the food. This means the food is the Jew's responsibility, and thus if it's Chametz, he couldn't have it in his house on Passover.