The Rambam writes (Hilchot Tefila 5:10) that there are five prostrations in each Amida prayer: One at the beginning, one at “Magen Avraham”, one at “Modim”, one at “Hatov Shimcha” and finally, one prostration as one is taking three steps back at the end of the prayer. One of the reasons for bowing as one takes the steps back is a sign of respect as one departs Hashem’s presence. The Ben Ish Hai (Beshalah, First Year, 24) holds, however, that as one takes three steps back one should only bow slightly. Rav Ovadia Yosef (Halichot Olam, vol. I, pg. 143) questions the Ben Ish Hai’s statement of only bending slightly, especially in light of the Rambam’s ruling that it must be a full-fledged prostration. The Orhot Zion reconciles this by saying that Ben Ish Hai agrees with the Rambam that one should bow down, but that this bowing does not have all the laws and details of the other prostrations in the Amida.
Summary: One should bow down as one is taking the the three steps back at the end of the Amida
Bowing When Taking 3 Steps Back