Example [by-によって] my [of-の] during-bath [to-に] phone [subject-が] rang.
入浴中 is a compact way to say 'while bathing, during the bath' — 中 ('during, in the middle of') attached to a verbal noun. 私の入浴中 ('during my bathing') functions as a temporal adverbial. The universal frustration of being interrupted mid-bath.