To what extent is there an inyun for Woman to be tzniyus in front of sefarim? Does it apply to her clothing? Covering her hair? What if there is only her husband there? Or only her young son? In a small apartment, it is very possible that there are sefarim stored in almost every room.
Answer:
There is no obligation for a man or woman to dress modestly in front of sefarim. However, one (man or woman) she should not be entirely naked (giluy ervah) in front of sefarim.
Sources: Magen Avraham (OC 45:2) writes that it is prohibited to stand naked in front of sefarim, a halachah he bases on a Gemara (Shabbos 120b), and on the laws of mezuzah. However, we find in the laws of mezuzah that only a room wheich is used on a regular basis in such a manner, such as a bathhouse, is exempt from mezuzah, whereas a room in which people are only sometimes nakes is obligated in mezuzah, indicating that there is no actual prohibition of appearing naked in front of the mezuzah. Moreover, with regard to sefarim today there is an element of doubt as to whether they possess the kedushah of handwritten texts (this is a dispute between Chavas Yair and Taz, see Mishnah Berurah 40:4, and see also Minchas Yitzchak 2:96-97 and Har Tzvi, YD 143). This is all the more true of modern publishing techniques which do not involve any human input (Maharsham 3:357). Furthremore, some authorities maintain that the sefer’s binding is considered a partition (see Daas kedoshim YD 285; Kaf Ha-Chaim 40:14; Mishnah Berurah 40:4; Pri Megadim 40:2; Maharam Shik OC 94; Maharsham (Daas Torah) 240:6). In addition, books are often placed on a shelf that is above 10 tefachim from the ground, which constitutes a partition according to some authorities (see Maharam Shik, OC 94). Therefore, there is room for leniency even with regard to being entirely naked in from of sefarim. However, out of respect for sefarim, one should not appear before them entirely naked, but there is certainly no obligation to observe the general laws of tznius (covering covered parts of the body) in front of sefarim.
