However, her hair is uncovered, which akin to nakedness, as it is highly
immodest for a married woman to appear in public with her hair
uncovered. Indeed, since she behaved like a beast, who has no concept of
modesty, her offering is of an animal-like food, barley.
As for the option of men "attending", I believe it was Rashi who warned
that any man who saw a woman involved in thr Sotah procedure should
become a nazir. Men attending was probably not encouraged. (The pesukim
about the Sotah immediately precede the pesukim about the Nazir).
Additionally, walking her around the Temple grounds was done the long
way, so that she would have time to think about her situation and, so
that the Kohanim might have time to discuss her situation with her.
Eliezer Gamerman (email@example.com)