May one enter Sefarim into a bathroom?
It is forbidden to enter revealed Sefarim or Tefillin into a bathroom due to it being a belittlement to the Sefarim. If the Sefarim are covered then at times it is allowed to enter the Sefer into the bathroom. This depends on whether the bathroom is a private bathroom or public, and as to whether they are covered with one covering or two.
It is forbidden to enter revealed Sefarim, or any books that contain words of Torah, into a bathroom. It is proper to be stringent even if one does not desire to currently do his needs in the bathroom.
If the Sefer is covered: It is forbidden to enter Sefarim into a private bathroom even if they are covered. [Regarding if the Sefer is in two coverings see Q&A!] It is permitted to enter with a Sefer into a public bathroom even if the Sefer only has one covering. However the covering is only valid if it is not designated for the Sefarim or contains a Tefach. It does not suffice to merely wrap the Sefer within clothing that he is wearing and hold it in his hand.
Public bathroom: It is permitted to enter Tefillin or Sefarim into a public bathroom if they are covered by an undesignated cover, and one is doing so to guard it from being stolen.
Private bathroom: Sefarim and Tefillin may never be entered into a private bathroom even if they are covered with an undesignated covering. See Q&A regarding if they are covered within two coverings.
May one enter Sefarim into a private bathroom if they are covered by two coverings?
If the Sefer is within two coverings many Poskim rule it is allowed to enter it into a bathroom. Others however rule one may never enter Sefarim into a private bathroom, even if they are doubly covered, being that one can leave them outside the bathroom without worry of them getting stolen. Practically the custom is to be lenient if the Sefer is within two coverings. According to all opinions a double covering is only valid if one of the coverings is not designated for the Sefer.
 See Admur there that they may not be entered into a public bathroom, or field unless they are properly covered. They may never be entered into a private bathroom or field even if they are properly covered. [See Q&A regarding a double covering]
 Admur ibid writes as follows: Whenever one enters a bathroom without intention of using it, there are opinions which say that one may even enter revealed Tefillin and Torah books, even by a bathroom in a private area, even if the bathroom is used for both urine and feces. However others say that if the bathroom is also used for feces, then entering for no need at all receives the same laws as one who enters to do his needs. Practically one should be stringent and suspect for this latter opinion. [ibid] Vetzaruch Iyun based on the ruling of Admur in the Siddur that it is forbidden to have Sefarim revealed in face of feces, if here too he would hold it is forbidden to enter improperly covered Sefarim into a bathroom [and not just merely a proper measure].
 This refers to a bathroom that is within a home and one is able to leave his belongings outside without worry of them getting stolen. [43/5]
 43/6 in parentheses: “(However in a bathroom that is in ones house they have the same law as Tefillin which are forbidden to be entered into it even if they are covered)”. This ruling of Admur is based on Michaber 43/7 which rules one may never enter Tefillin into the bathroom even if they are covered, and so rules Admur in 43/5. In 43/6 Admur applies this law also to Sefarim. This opinion of Admur is brought in Shaareiy Tziyon 43/17; Kaf Hachaim 43/28. So is implied to also be the opinion of the Elya Raba brought in M”B 43/25.The Kaf Hachaim ibid concludes that one is to be stringent like Admur.
The reason: As since one is able to leave the Sefarim outside the bathroom, in the house, therefore there is no allowance to enter them into the bathroom for no need. [43/5 regarding Tefillin and Admur applies the same rule to Sefarim]
Other Poskim: There are Poskim that rule it is permitted to enter Sefarim even into a private bathroom, if they are covered with a non-designated cover. [M”B 43/25 based on Radbaz; Peri Megadim 43 A”A 14] The M”A 43/14 states it is permitted to enter covered Sefarim into a bathroom, although he does not mention if this includes even a private bathroom.
 This refers to a bathroom that is within a public area and one is hence unable to leave his belongings outside due to worry of them getting stolen. [43/5]
 Ibid based on M”A 43/14 and so rules Shesilei Zeisim 43/26; Kaf Hachaim 43/28 nevertheless the Kaf Hachaim ibid concludes that if one is able to guard the Sefarim outside the bathroom he is to be stringent even then.
The Reason: As if one were to leave it outside there is chance of it getting stolen. [43/5]
 43/4; Michaber 43/6; If the Sefarim are covered by their own designated covering [i.e. a covering that was designated to be used for the Sefer] then it is nullified to the Sefer and the Sefer is considered as if it was uncovered. If however the cover has a Tefach of space then it is not nullified to the Sefer. [Admur ibid] The reason why if it has a Tefach it is valid is because it is considered like an Ohel. [M”A 43/13] Vetzaruch Iyun as to the definition of a Tefach. Does it mean a Tefach of space that is hovering over the Sefer, such as if the Sefer is in a box or does it mean that the vessel has the total space of a Tefach inside? Seemingly the former is correct and only if the bag contains a Tefach of width and a Tefach of hovering space over the Sefarim is it considered an Ohel. [see 315/17]
 43/6; This allowance was only given by Tefillin. The reason why Tefillin are more lenient than other Torah books in this regard is because Tefillin are constantly with a person and thus the sages did not want to require a person to have to constantly go home to put away his Tefillin before entering a bathroom. Torah books however can initially be left at home, and therefore the sages did not feel the need to be lenient. [ibid]
 Ruling in Shulchan Aruch: The concept of entering a Sefer with a double covering into a bathroom is not mentioned in Shulchan Aruch. It however is mentioned in 40/3 regarding having Tashmish in a room with Tefillin; 40/8 regarding having Tashmish in a room with Sefarim. Michaber 240/6 regarding having Tashmish in a room with Sefarim; Admur 315/5 regarding having Tashmish and doing ones needs in a room with Sefarim. In all these Halacha’s it is ruled that a double covering permits the act.
 Machatzis Hashekel 43/14; Elya Raba brought in M”B 43/25 and so rules M”B ibid bringing an opinion that is lenient even if it only has one undesignated covering. So concludes Piskeiy Teshuvos 43/3
Ruling of Admur: in 43/6 Admur simply writes it is forbidden to enter Sefarim into a private bathroom even if they are covered. He does not mention a difference between two coverings or a single cover. However in 315/4 Admur rules one may do his needs in front of Sefarim that contain two coverings, hence implying like the opinion of the Machatzis Hashekel that two coverings always permit the entrance of Sefarim. However perhaps one can say that case is different as we do not require one to take the items out of his room in order for him to do his needs and rather suffice with a double covering, just like we rule by Tashmish. However to initially enter the Sefarim into a bathroom perhaps Admur never agreed that it is allowed. Vetzaruch Iyun.
 Kaf Hachaim 43/30 based on Ateres Zikeinim 43 regarding Tefillin and seemingly the same would apply regarding Sefarim, as rules Admur 43/6 that they have the same law as Tefillin regarding a private bathroom.
 Heard from Harav Asher Lemel Hakohen, and so is the custom.
 Admur 40/3 based on Michaber 40/2