busy as a bee

bee in one's bonnet

Something of particular interest or concern; an obsession.

busy as a nailer

working constantly.

busy work

Work or activity performed with the intention or result of occupying time, and not necessarily to accomplish something productive; routine work of low priority undertaken for the sake of avoiding idleness.

get busy

To have sex.

keep someone busy

To ensure that someone's attention is occupied, often to prevent them from becoming bored or noticing something.

queen bee

The most important or dominant woman in an organization or situation.