There are many synonyms that can be used interchangeably with the phrase "bad smell." Some common substitutes include stench, odor, foul scent, noxious fumes, malodor, funk, pungent aroma, reek, and musty aroma. Depending on the context in which the phrase is used, some of these words may be more appropriate than others. For instance, "stench" suggests a very strong and unpleasant odor, while "funk" is more casual and can refer to a range of unpleasant smells. Ultimately, the particular synonym chosen will depend on the speaker's intended tone and purpose, as well as the exact nature of the smell being described.