Is it permissible for a younger person to bow to an older person when greeting him?
Question

The issue of the shirk of respect is very confusing for me. We have a tradition among our relatives that the younger person will bow slightly to his elders, at which point the elders will place their hands on the heads of the younger people as an expression of love, but the younger ones do not bow as the Muslim bows in his prayer.
Praise be to Allah.It is not permissible to bow when meeting anyone, whether he is a scholar or otherwise. 
Shaykh al-Islam Ibn Taymiyah said: 
With regard to bowing when greeting someone, it is not allowed, as it was narrated in at-Tirmidhi that they asked the Prophet (blessings and peace of Allah be upon him) about a man who bowed when he meets his brother. He said: “No (do not do that).” That is also because it is not permissible to bow or prostrate except to Allah, may He be glorified and exalted, even though doing this by way of greeting was acceptable according to the teachings of earlier Prophets, as in the story of Yoosuf, “…and they fell down before him prostrate. And he said: "O my father! This is the interpretation of my dream aforetime…” [Yoosuf 12:100]. But according to our laws (sharee‘ah), it is not acceptable to prostrate except to Allah. In fact there is even a prohibition on standing up in greeting for one another as the non-Arabs do, so how about bowing and prostrating? That which is a partial bow is also included in the prohibition.
End quote from Majmoo‘ al-Fataawa (1/377) 
And he said: 
With regard to lowering the head before elders such as shaykhs and others, or kissing the ground in front of them, and the like, these are things concerning which there is no dispute among the leading scholars that they are prohibited. In fact merely inclining the back to anyone other than Allah, may He be glorified and exalted, is prohibited. In al-Musnad and elsewhere it is narrated that when Mu‘aadh ibn Jabal (may Allah be pleased with him) returned from Syria, he prostrated to the Prophet (blessings and peace of Allah be upon him and his family), and he said: “What is this, O Mu‘aadh?” He said: O Messenger of Allah, I saw them in Syria prostrating to their bishops and patriarchs, and they attributed that to the teachings of their Prophets. He said: “They are lying, O Mu‘aadh. If I were to instruct anyone to prostrate to anyone, I would have instructed women to prostrate to their husbands, because of the rights that Allah has given them over them. O Mu‘aadh, do you think that if you pass by my grave, you would prostrate?” He said: No. He said: “Then do not do this” – or words to that effect. 
Conclusion: 
Standing up, sitting, bowing and prostrating (which are actions done in the prayer) are due only to the One Who is truly deserving of worship, the Creator of the heavens and the earth. Whatever is due exclusively for Allah cannot be directed to anyone or anything else in any way, as in the case of swearing an oath by anything other than Allah, may He be glorified and exalted. 
End quote from Majmoo‘ al-Fataawa (27/92-93) 
For more information on the issue of prostrating to anyone or anything other than Allah, please see the answer to question no. 229780 
And Allah knows best.