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...

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 :

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2. What does Scout mean when she says “I was  
 worrying another bone”?

2. Scout is concerned with
something else.