Is it Haram to bend (as when you are praying) for a person like a king?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Yes, bowing to someone as mentioned in the question is forbidden regardless of who he is. Whoever he may be, he will never be more honorable, more significant and more complete than the Prophet Muhammad (Sallallahu Alaihi wa Sallam). In spite of the deep affection, great honor and utmost love of the companion to the Prophet (Sallallahu Alaihi wa Sallam) they used not to stand for him much less the act of bowing. Anas (Radiya Allahu Anhu) said: "No one was dearer to them (the companions) then Allah's Messenger (Sallallahu Alaihi wa Sallam), but when he entered upon them they did not stand up because they knew his dislike of that" . Besides it, bowing for kings or leaders is the custom of polytheists whereas we are ordered to be different from them in all matters. There are many proofs that establish this fact. Sheikh al-Islam Ibn Taymiyah (may Allah's Mercy be upon him) discussed this matter extensively in his famous book 'Iqtiza al-Sirat al-Mustaqeem Fi Mukhalafat Ashab al-Jaheem'.
Allah knows best.