ANSWER:

She is sinful for being in such a position in the first place and for responding to that man’s gesture and for nodding her head like that! This is not kufr but sinful.

If a stranger man extends his arms to shake hands with a muslim woman, then she bows her head down lightly and apologises to reject shaking hands, is this light bowing down of head only without back (not ruku’) considered haraam or shirk ? Knowing she is only doing it to reject politely, and only lightly tilting her head without back and not doing full ruku’.