With regard to Torah study while unclothed, the halachah distinguishes between verbal and silent learning. Although it is forbidden to speak words of Torah when one is undressed, one may think words of Torah in his mind under such conditions. In the same way, it is permissible to hear words of Torah – without speaking them – when one is not wearing clothes. In principle, then, it is permissible to hear words of Torah – either live or recorded – in the bath or shower.
It should be noted, however, that it is forbidden to even think Torah matters silently in a restroom. Restrooms contain a kind of spiritual tuma and one may therefore not even think or hear words of Torah in the restroom. Hence, if one’s shower is situated in the restroom, it is forbidden to think or hear words of Torah in the shower.
This is stated by Rav Ovadiyah Yosef shlit”a. He adds that this ruling applies only in private showers, such as the shower in one’s home. Public bathhouses have a different status, and one may not think or listen to words of Torah in a public bathhouse or shower.