。
She bowed her head to me politely.
Literal
She [topic-は] me [to-に] politely head [object-を] lowered.
頭を下げる literally means 'to lower one's head' — the physical act of bowing. By extension it also takes on figurative meanings: 'to apologize,' 'to humble oneself,' or 'to ask a favor.' Bowing in Japan is socially graded: a quick 会釈 (a small nod) acknowledges someone in passing; a 30° 敬礼 marks ordinary politeness; a 45° 最敬礼 is reserved for serious apology or deep gratitude. Parents sometimes counsel their children 軽々しく頭を下げるな ('don't bow lightly') — bowing is something you mean. With 丁寧に here, the gesture is unambiguously a polite, intentional bow rather than a figurative apology.