Antonyms for the phrase "doing one's bit" would involve not doing anything at all or actively refusing to contribute to a cause. Antithetical phrases may include "dragging one's feet," "sitting on the sidelines," or "leaving the heavy lifting to others." Other antonyms could be "ignoring the issue," "failing to step up," or "opting out of responsibility." These phrases suggest a lack of effort, commitment, or concern towards a situation, issue, or cause that requires action. In contrast, doing one's bit implies a willingness to take part and make a difference, no matter how small.