How do you not let something bother you?
Your question is actually part of your answer; You are in control of your thoughts and moods; if you are bothered by someone or some thing, it's because YOU CHOOSE to let it bother you; OTHERWISE, some one or some thing controls your moods and not yourself. If you can change what bothers you, then do so; If you cannot change it, then, realize it's in the same category with things like, the weather; you can't change it, so you adapt and accept it. Hope this helps.
I would like to add that in fact we have self will, this self will must be accompanied by auto distancing from your OWN emotions, to put it plainly, step back, count 1,2,3,4,5,6 then think...why do I feel angry? who makes me angry, his words or MY EMOTIONS? I agree with the statement above, only YOU can control your OWN emotions, and while I am at it , YOU CANNOT EVER CONTROL OTHERS EMOTIONS OR ACTIONS. You can only change yourself. Sounds simple? It is, but why don`t people do this, because it requires you to ananlyze the reasons why, somehting that people don't want to do because it requires admitting somethings, that well, we don't want to. In fact, this is an excercise in emotional intelligence spoken by Daniel Goleman, who is the foremost expert on the subject. In fact, you can put his name along with "emotional intelligence" and you will find lots of info on him.
P.S: I AM A PSYCHOLOGY MAJOR TAKING ADVANCED COURSES.
"Mind over matter" -- If you don't mind than it doesn't matter.
I know that sounds overly simplistic, but if you really think about it, it is that simple.
watch Oprah she'll give you motivation to think about a 'bigger picture' [usually] P