Generally speaking, 忙 is used in both daily speech and writing, while 忙碌 is usually used in only writing. According to currently prevalent Chinese grammar, both of them are adjectives, rather than adverbs. In Chinese a single adjective often act in different sentences as attribute,predicate or adverbial: 贝丝是个大忙人 || 贝丝很忙 || 看到报纸烧着了,贝丝忙把一杯水浇在火苗上。To serve as an attribute, the use of 忙 is very limited. It appears only in some quite fixed expresions such as 忙人,忙音,忙月. From another point of view, we would rather say 忙 cannot be used as an attribute. .......... 忙着... 忙忙碌碌