I'm angry at a "depressed girl"
How are you going to handle the situation with her?
I'm going to politely ask her to stop doing that
Even though her behavior might be upsetting you, you need to be more understanding that she is going through some things. People will think you are a bully if you mess with a depressed girl.
Why don't you mind your own business and let me bully her if I want to?
Because bullying is wrong and should always be called out. You should move on from her and let her be.