。
She asked me about my mother.
Literal
She [topic-は] me [to-に] mother [about-について] asked.
Note the dual use of 私に here — 私に marks the speaker as the recipient of the question (she asked him), and 母 (without 私の) is the mother being asked about, with 私の implied by context. The compound particle ~について ('about, concerning') marks the topic of the question. The 私に + ~について split is a subtle but characteristic feature of Japanese argument structure: one に for direction-of-speech, another particle for topic-of-speech. たずねる (尋ねる) is the slightly deliberate, formal counterpart to the everyday 聞く.