Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
It is not permissible for a ruler to order his subjects or citizens to bow to him.
Imam Ahmad and Abu Dawud reported in a Hadith that Mu’wiya passed by Ibn Zubair and Ibn Amir. Ibn Amer stood up and Ibn Zubair remained sitting. So Mu’wiya told Ibn Amer I heard the Prophet (Sallallahu Alaihi wa Sallam) saying: "Whoever wants people to greet him by standing will be admitted to Hellfire."
So, if this is the case of a person who wants people to stand to him when greeting him and does not order them to do so, then what about a person who orders his subjects to bow to him.
The scholars, may Allah have Mercy on them, discussed the issue of bowing to other than Allah, in the chapter of apostasy and whether the person who does so, comes out of the fold of Islam or not. They discussed the reason why they distinguished between bowing and prostrating. They all judged and determined that whoever prostrates to other than Allah becomes a Kafir, as prostrating is only allowed to Allah, and this is different from bowing.
The learned scholar, al-Bujayrimi, may Allah have Mercy on him, said in his footnotes of the book Sharh-al-Khatib: 'If someone prostrates to a creature like an idol, he becomes a Kafir, except if he does so by necessity, like in a Kafir country where he was ordered to prostrate, and he feared for his life. But if he only bows down (to the idol), he does not become a Kafir by doing so as long as he does not believe in other than Allah.'
However, if he intended by bowing to other than Allah glorifying and praising him like Allah, then he becomes a Kafir.
And if a non-prisoner prostrates to an idol in wartime, he becomes a Kafir. However, bowing is not like prostrating, as bowing is usually performed to a creature, and this is not the case of prostrating, this is in general. Anyway, if one intends to glorify a creature by bowing to him, like he/she glorifies Allah, then there is no difference in this case and therefore such a person becomes Kafir.
In conclusion, bowing to a creature like when meeting important personalities is Haram in general, if one intends to glorify them but not in the same way one glorifies Allah. However, one becomes Kafir if he intends to glorify them in the same way one glorifies Allah.
Allah knows best.