How to not let it bother you? Easy, leave your ego at home. It's not always about you, it's not personal, and people aren't talking loudly to purposely mess you up. Everyone has their own little world before they come to the bowling alley. Some are there to meet up with friends they see once a week, some are there for the competition, some the beers, some to relieve some stress as they might work a job that puts them under a great deal of stress (Cop, Firefighter, EMT, Lawyer, Salesman, Small Business Owner).
Bowling is supposed to be sociable, fun, and above all a game. When I say leave your ego at home, it's not a personal direct insult. Our ego's are telling ourselves all day "ME, ME, ME!" "This happened to ME, because someone did ___", "This person is making ME upset with their indirect actions". Take the "Me" out of it and instead of focusing on the loud talking behind you tell yourself this:
"I am here in a competitive setting. There's going to be loud noises, there's going to be people talking, there's going to be random screams. This is the environment I am in for the night and it is up to me to make the best shot that I can make now".
Envision the entire shot before you throw it, and as soon at the ball "strikes" in your head, go.
This was something I used to struggle with a lot until I learned to let everything else go around me and it's a coaching technique that a lot of team sports coaches use. Especially basketball coaches in free throw drills where you have to make a shot among the noise of hundreds to thousands of people in the arena with you. Good luck.