Sam, once again you are right on the money. You can’t make general rules here. Each woman does what her own Rav paskens for her.
As far as a boss legally permitted to say it, a boss can ask whatever they want, demanding it or making it part of the dress code, no I don’t believe he has the right to do so. Could he demand that of a non-jew taking the same position? No, not unless it was a safety issue. He could have a dress code which would require a woman to dress in a modest fashion covering their chest, arms and legs as long as he provided enough air conditioning and temperature control to be comfortable to accommodate that dress code. But to require head covering, no that would not fly.