There are numerous synonyms available for the phrase "do a bit" that can enhance our vocabulary. Some of the alternatives to this phrase include "perform a little," "carry out a small task," "take care of a minor job," or "accomplish some work." Other options include "execute a portion," "handle a task partially," or "fulfill a portion of the work." Additionally, we can use phrases like "complete a portion," "address a part," "get through a bit," or "deal with a bit of work." Using these different synonyms can help us to express ourselves more effectively while conveying the same meaning.