Is it permissible to listen to Jewish music or to a shiur while taking a shower?
To make things clear, you are asking regarding listening to pesukim or a torah shiur, which you are not talking torah words, but rather only thinking torah thoughts. We have to differentiate between different situations. If the shower is in a room that has a toilet, then it is considered a like a bathroom and we should not think in learning, listen to a shiur etc. in such a room. Additionally if the shower is in a public type of room that there are a number of showers there, or a mikva, it is also not permitted. The reason being because there is a lot of steam and grime there, therefore we should not be thinking in learning their either. If however the room is only a shower room, and it is kept clean, especially if it is a shower room and also used for other uses, such as storage, laundry, etc. then, although it is controversial. A number of poskim hold that it is still considered a bais hamerchatz, however according to a number of poskim it would be permitted. Ideally, hurry up your shower and listen to your shiur afterwards.
Chasam Sofer Y:D 207, V’yashav Moshe 1-58, H-shem Ohr Li 1, Mamar Mordichai (R’ M. Eliyahu zt”l ) 14-108, Piskei Teshuvos 84-4, Poskim.