Concern and worry I feel go together/ can sometimes be interchangeable. Sometimes one fits better than the other. Example: I am concerned about his health or I am worried about his health. I am worried about my final grade. I am concerned my final will affect my grade poorly. (again you could change these around) Bother is usually in regards to interrupting when you are doing something else sometimes only once or constantly/continuously. Example: "Please, stop bothering me when I am on the phone" I might tell my kids. Please stop bothering me about candy in the store, we don't have the money for it. One might say " I don't want to bother (meaning bug you) but I need something (password, help, etc).

It would be "I'm not bothered" = I don't care and "It doesn't concern me" = I'm not worried about it. Being bothered is very similar to being disturbed by something in a sense and in another, it's like caring.