Is it permissible to use a bus designated for a women's Quran memorization center to transport mosque students to the Tarawih prayer in different mosques?

The supervisor of the Dar (Quranic school) must manage its buses in a way that serves the interests of the Dar. Indeed, anyone who acts on behalf of another must act in their best interest. You did well by not allowing the mosque students to be transported to Tarawih prayers in the women's Dar at-Tahfeez bus, because this is not in the interests of the Dar.

If the bus is an endowment (waqf), then reference must be made to the conditions set by the endower. If it was endowed specifically for the women's Dar, then it should only be used for matters related to the women's Dar. However, if it was endowed for the "complex" in general, then it can be used for matters serving the interest of the complex, which includes transporting students for Tarawih prayers. The conditions of the endower must be followed as long as they do not contradict Sharia (definition), and it is impermissible to use vehicles belonging to charitable institutions for personal purposes.