Thinking about this further, and this manager’s behaviour, I’d suggest an email using work email addresses which says the following.
“Dear X
Due to personal reasons, which are of a confidential nature, I am no longer in a position to drive you home from work.
Best wishes, X”.
If she emails back to ask why, reply with:
“As explained, for personal reasons, of a confidential nature, which I am not in a position to discuss.”
Give no further explanation or information.
If she keeps up the questioning, reply with “I have no wish to cause you offence - and I am of course very conscious that you are in a more senior grade than I am - but I’m afraid that, as explained, it’s for personal reasons, of a confidential nature, which I am not in a position to discuss.”
If she asks you face to face, repeat that same sentence.
If she gets someone else to ask you, say the same thing.
And make sure you join a trade union.