Is it permissible to listen to lectures or the Quran via Bluetooth headphones while showering, whether the mobile phone is inside or outside the bathroom?

It is not permissible to recite the Quran in a place where one relieves oneself, as this contradicts the veneration of Allah's words. The place for relieving oneself is a place for impurities and the uncovering of private parts.

As for listening to it, if the sound source is from outside, there is no objection. However, if it is from inside, it is similar to reciting in the bathroom, and it becomes forbidden, either by way of prohibition (tahrim) or severe disliking (karahah shadia). It may also lead to prolonging one's stay while relieving oneself, which is forbidden. It is disliked for one to speak or recite [in the bathroom], not for one to listen from a recorder outside the bathroom. It is preferable to entirely avoid the intention of listening to the Quran in this place and to occupy oneself with something else beneficial.