[英文]with an air of busines

air = the way somebody does something (樣子, 神態)
business = responsibility; something that concerns a particular person (職責, 本分; 分內事)

She walked with an air of business
= 她帶著一副凝重(戰戰兢兢)的神情走著。

She normally walk and go about with getting down to business,not be influenced by friendship in office, that business is business.