I actually understood more or less what Scout was talking about in To Kill a Mockingbird, but I wanted to be sure about the meaning of the idiom...
"...worrying a bone" or "worrying another bone". Chapter 9.
I believe the idiom of "worrying another bone" is related to the idiom of having "a bone to pick." Some people use the idiom of having a bone to pick to mean that I have something to discuss with you. This discussion can be quite serious and unpleasant. In much the same way, Scout is saying that she has something else to say to Atticus. She has a question to ask and it is serious and unpleasant. It is something that will worry him. She has talked with Atticus on many occasions. On this occasion, she has "a bone to pick." In other words, she is "worrying another bone" which means she has another worrisome or disturbing question to ask Atticus.
In a study of these questions, the question and answer is below and can be found under To Kill A Mockingbird Quizzes at enotes.com:
2. What does Scout mean when she says “I was worrying another bone”?
2. Scout is concerned with something else.
This passage comes in Chapter 9 of To Kill a Mockingbird when Scout is once again trying to convince Atticus that she doesn't need to attend school. But Scout realizes that debating the subject with her father is like "worrying another bone." This is an old phrase that literally means
"To seize with the teeth and shake or tug at repeatedly: a dog worrying a bone..."
Rhetorically speaking, however, it reflects on the argument that Scout and Atticus have had before about school--a verbal tug-of-war and back-and-forth debate that Scout knows she will not win. The idiom is similar to the one about "flogging a dead horse"--it's a useless action with predictable results. Thus, her statement about the "bone," followed by her changing the subject to that of lawyers defending Negroes.