person with a bad reputation is correct because black sheep means a person who is regarded as different, troublesome, or disreputable within a group or family.

This idiom or phrase is useful because it helps students understand the intended meaning beyond the individual words.

Examples: He was considered the black sheep of the family because of his dishonest behavior. Every group may have a black sheep who damages its reputation.

The idiom focuses on reputation in a group, so the best option is the person with a bad reputation.