If she's too intimidating to approach in person, could you perhaps post a note through her door, in a friendly tone?
I realise it's very sycophantic, but if all else fails:
"Dear X,
This is a note of apology, in case you were disturbed last night.
I've been having trouble sleeping recently, and, as I need to have a sharp mind for work, I hoped some soothing music might help.
However, my stereo was set at its daytime volume, far too loud for the night hours. I quickly turned it down, but, what with our adjoining wall being so thin, I fear you may have been awoken at around 1am.
I assure you it won't happen again.
Yours, GetOffMyDoorJack