Why is Mildred worried about being caught with books? What does this tell you about her character?

Mildred is worried about being caught with books because they are against the law. She doesn't want her house burned down and sees Montag's actions as foolhardy. These actions show Mildred as a law abiding citizen who conforms to the dictates of the law.

As Jill d said she is worried about being caught with books because it is against the law and she doesn't want her housed to burn. This show me that she is Selfish because instead of supporting he husband she tell about Montag having books to the cops or someone else. Therefore, she is selfish and think good about herself but not her husband.