If by moving or bowing his head it can make one who dhikr more solemn’, then this is better for him. However, if he is more solemn, without bowing his head or moving him, then dhikr with a state of silence is better for him. And if both of these conditions, namely silence and moving or bowing their heads, are equally solemn, then for him may choose silence or with movement. (Fatawi al-Khalili ‘ala Madzhab al-Imam as-Shafi’i, 36)
Imam Kholili was asked about what people do such as bowing and moving (the head) when reading dhikr and so on, is this basic in sunnah or not? Is it haram, makruh, sunnah or is there a reward? Is it the same as a person who resembles a Jew or not? Imam Kholili replied, when you understand the word of Allah: “They are those who dhikr to Allah while standing or sitting or lying down” (Qs. Ali Imran: 191). And the word of God, “Men and women who say much of Allah” (Qs.  al-Ahzab:35).
The movement in dhikr and reading is not something that is forbidden or forbidden, but it is recommended in some circumstances such as standing, sitting, lying down, moving, being quiet, traveling, being at home, rich and poor.Â
Imam Kholili said, “Dhikrk to Allah in standing, sitting, or lying down, night and day, in the seas and on land, in traveling or at home, in rich or poor, healthy or sick, in a state of sirri or overtness, and in all circumstances.Â
Then he said: how many people who dhikr silently forget, but when he moves he remembers (his dhikr), thus moves more foremost for him. How many people are dhikr and how many dhikr are moved so that the movement eliminates its specificity, this silence is better (for him).
How many who dhikr or who read, the two circumstances (moving or silent) become the same for him, so he does what God wants, and Allah shows those whom He wants on the straight path, and for every ummah there is his qibla (himself) that he faces him. So you will be good.  Wallahu a’lam. (Fatawi al-Khalili ‘ala Madzhab al-Imam as-Shafi’i, p. 36)