Special care must be taken to protect the honor of sacred books, such as Siddurim, Humashim, and all books of Torah literature. It is strictly forbidden to allow bodily waste in the presence of sacred books. When young children are being toilet trained, parents must not allow the children to use the portable "potty" in a room containing sacred books, and doing so constitutes a grave infraction on the honor of these texts.
The Mishna Berura writes about a family that kept a bedpan in a small room which they used as a restroom, and the stench spread into the main room where there were Torah books. The family suffered as a result – the homeowner's son abandoned religious observance, and the family endured considerable humiliation. The Mishna in Pirkeh Abot (4:6) warns that one who disgraces the Torah will be punished with disgrace, and the Mishna Berura pointed to this unfortunate incident as an example of such a transgression. Hacham Ovadia Yosef, in his Anaf Etz Abot, likewise applies the Mishna's warning to those who fail to show proper respect to Torah books, such as by placing a child's potty in their presence, or having marital relations in a room with Torah books.
(It is similarly customary not to allow young children near the Shabbat candles when they are unclothed, due to the sanctity of the Shabbat lights.)
Many people carry small books or papers in their pockets throughout the day – such as a small Siddur for Minha, a small Birkat Ha'mazon, or a pocket-sized Gemara or Torah pamphlet. If one has such a text with him when he needs to use the restroom, he should remove the sacred text from his pocket before entering the restroom. If this is not possible, such as if one is in a public area, then he may enter the restroom with a book in his pocket. A sacred book may be brought into the restroom if it is under two coverings, and when necessary, one may consider the binding one covering, such that the pocket is considered the second covering. Preferably, one who often carries a small Siddur or Torah book with him should wrap it with an additional covering. If one keeps a small Birkat Ha'mazon card in his wallet, he is certainly permitted to enter the restroom with the wallet, as the wallet is considered one covering and the pocket is considered the second.
A woman who wears a piece of jewelry bearing the inscription of a verse from the Tanach must remove it before entering the restroom. If the jewelry features only a name, it may be brought into the restroom.
It is certainly permissible to bring a phone or other device into the restroom even though it contains Torah content, because that content is not being displayed at that time.
One who keeps a picture of a Rabbi with him in his pocket may enter the restroom with the picture, as pictures have no Halachic status of sanctity. Of course, one must not treat such pictures disrespectfully, but keeping them in one's pocket in the restroom is permissible.
Summary: It is forbidden to allow the presence of bodily waste in the presence of sacred books, such as Siddurim or any books of Torah literature, and therefore young children must not be potty trained in a room where sacred books are present. If one carries a sacred book in his pocket, and he cannot leave it outside when he uses the restroom, he may bring it in his pocket to the restroom, as the binding can be considered one cover, and the pocket is then the second required covering. Preferably, though, the book should be wrapped with an additional covering. One may enter the restroom with a Birkat Ha'mazon card in his wallet, as the wallet is the first covering and the pocket is the second. A woman who wears a piece of jewelry bearing the inscription of a verse from the Tanach must remove it before entering the restroom.