I have searched, and seen some type of questions related to this. However, I have seen no sources. I figured I would ask: does anyone know of any sources for bowing during 'zeh el zeh v'amar"? Why do we do it?
An answer is provided here:
Hatefilah Vhilchoteha 2:314 quotes Rav Ovadia Yosef and Rav Chaim Kanievsky that there's no basis for the minhag to bow during vkara zeh el zeh v'amar. Az Nidbaru 13:32:3 agrees. He says for those who do it can bow either to the right first or left first but what is important is to pay attention to the words. Shivat Tzion Shabbat 7:106 v. 2 p. 117 writes based on the zohar that the angels when praising Hashem turn to the right first and then to their left and in kedusha we're mimicking the angels. He explains that it isn't similar to Yoma 53b where we're leaving Hashem's presence.1 Rivevot Efraim 5:103:2 writes that one should turn to the right first and the left. Hatefilah Vehilchoteha ask quotes the Mayim Chaim 2:7 who writes that one should first turn to the right since one isn't taking leave of Hashem.
There are a few more reasons cited here
They seem to centre around requesting permission from the angels to praise Hashem:
The Siddur Tefila L'David of the Lelover Chassidim says that when one is reciting the "V'kara Zeh el Zeh V'amar" one should bow to the right and then to the left as if one is taking permission. [Cited in Minhag Yisrael Torah O.C. 125:2]
The "permission" in this context is open to a number of different interpretations. One will note that the opening line of the Kedusha is a declaration of our desire to praise God just like the angels do. We are told that when the angels praise God with the thrice "Kadosh", they first call out to each other in order to organize themselves to praise Him in unison. We can suggest therefore that our bowing to the right and left is intended to humble ourselves and request permission from these angels, often depicted as standing on either side of God, to praise Him as they do. [Yeshayahu 6:3]
Another cited source for the "V'kara Zeh El Zeh V'amar" movements is a reference to the piyut "Amitzei Shechakim" that is recited on Yom Kippur which makes mention of angels turning to "every side" to recite the "Kadosh". Again, it would appear that the desire to imitate the angels at this time is seen as a commendable act which likely fueled the "V'kara Zeh El Zeh V'amar" customs. There is also a basis for the practice based on the Zohar [Parshat Noach, cited in Minhag Yisrael Torah O.C. 125:2] which relates the bowing to the right and left to the rainbow. [Cited in Minhag Yisrael Torah O.C. 125:2]
It is also worth noting this here which reiterates the above.