"The music does not bother me at work."
I think "The music does not bother me at work." and "Music doesn't affect my work" have different meanings. In the former, the music doesn't bother you, in the latter, maybe it bothers you, maybe it doesn't, but regardless there is no impact on your work. So which one is the given translation closer to?
I think that the key issue here is that "work" (工作) is not a place in Chinese, only a verb. So, there is no direct way to translate "at work" into Chinese. You have to translate it either to a specific place where you work (such as "at my office") or to the action of working itself, as we see in this Chinese sentence.
I also misinterpreted this sentence. The apparent intent is to say, "Music doesn't bother my work." Another way a native might say this would be, "The music at work doesn't bother me." The English given is an acceptable sentence, but it doesn't match the apparent intent of the Chinese.