WTP- I don’t see why it’s untznius though. It just might be uncomfortable for her the first few times she goes out, but after that she shouldn’t mind. I certainly don’t care anymore if people know I’m going on a date.
Even if you don’t take public transportation, they can see you when you are in the hotel lobby or they can see the guy when he comes to the door or they can see both of you as you are walking to the car (that sounds even more awkward to me! How do people manage that?)