My right bumper is broken

I'd say, start by taking the controller apart and give it a good cleaning.

There are good disassembling guides on youtube. Remove the bumpers and scrub the plastic parts with water and washing-up liquid. You can also use a cotton swab with rubbing alcohol to clean the inner frame and around the button (where you do not want to use water).
Use an online gamepad tester to test afterwards. Then you'll easily see if the problem is gone.