Vigor, your last attempt seems dejecting. It's like from "Красная плесень": "Девки, вы пер******сь?" Sorry for my incontinence. I didn't mean it.

Kalinka's attempt with одиночество is a very sly idea, but no way to work. It must be so specific a situation to get it flush both of you. In an ordinary situation she would give you a look, with which you would feel yourself a second-hand lover.

In my opinion you can't make a short, compact phrase to enclose the meaning you want.

I could propose to come up to her, give a cough, to burble something, to hesitate for some time, to keep calm for a moment, then ask about the weather and finally shock her: "Извиняюсь за нескромный вопрос: ты ни с кем не встречаешься?"