The reason for selecting option (3) "Bitter relations" as the most appropriate meaning of the idiom "Bad Blood" is that this idiom is commonly used in English to describe ongoing hostility, animosity, or negative feelings between people or groups. It represents a situation where there is tension and resentment in their relationship.

1. "A sick person" : This is a literal interpretation of the words "bad blood," but it does not capture the idiomatic meaning of the phrase.

2. "A bad character" : This interpretation doesn't capture the commonly understood meaning of the idiom. "Bad blood" typically refers to interpersonal conflict rather than a person's character.

4. "A disease" : While "bad blood" historically referred to a medical condition involving an imbalance of bodily fluids, this meaning is less common today, and the idiom is more commonly used to describe interpersonal conflict.