Among the miracles of the Bais HaMikdash which the gemara describes (Yoma 21) is that when everyone came to Yerushalayim for aliya la'regel there was standing room only in the Mikdash, but miraculously there was sufficient space for everyone to bow. Why was this bowing necessary and why was extra space needed? Rashi explains that the miracle was needed so there could be 4 amos of space between each individual when reciting viduy (done while leaning over) so no one would overhear his/her neighbor's confession. The Maharasha offers a different reason for the extra space. Bowing in Mikdash was done as a response to hearing the Shem Hashem pronounced by the Kohein Gadol during the avodah of Yom haKippurim, just as we bow on Yom Kippur when we read the re-enactment of that avodah during Mussaf. This type of bowing entailed prostrating oneself on the floor, which takes up much more space than standing erect. The focus of Rash as well as the Maharasha seems to be on acts which we associate with Yom Kippur depsite the fact that the gemara refers to the miracle as occuring on aliya la'regel.
The Brisker Rav suggests that bowing was not a function of viduy or of hearing the Shem Hashem, but was a separate obligation incumbent upon anyone who visits the azarah. The GR"A comments on the pasuk in this week's parsha, "v'histachavisa lifnei Hashem Elokecha", that bowing is not as part of the halachic procedure of delivering the bikurim, but part of the ceremony of entering or leaving the Mikdash. Similarly, the Brisker Rav explains that this is why we say in our davening on the shalosh regalim we ask Hashem for the opportunity, "v'na'aleh v'nera'eh v'nishtachaveh lefanecha", to go up and appear in the Mikdash and bow there.