Much Ado About Nothing is a play of Shakespearne that is an archival sentence and quite literary.We can interpret it in Chinese as: "無事忙". But "Bu Jie Teng" is a Chinese slang stemmed from the backward cultural area. They cannot match each other eithr in style or in meaning.
I think the most applicable meaning of "不折騰" better be:"To the point, don't beat around the bush"!