mrsa is just multi resistant staphyloccocus aureus, a strain of the s.aureus bug that is resistant to most antibiotics (little fuckers are hard to kill). it isnt way more infectious than other bugs, and your immune system should kill it quite nicely, but you dont have antibiotics to back you up if you are immunocompromised. its not like its a super bug thats going to make you rot, its just hard to kill in the case of a shitty immune system
this bug isnt just found in your nose, its on skin as well. all over the place really
anyway, cut a long story short, all it would take is your gym owners spraying everything down at the end of the night with some methylated spirits or some other disinfectant (i love metho, it just kills eveything in sight and dries clean), particularly vinyl if it is cracked, and the handles of bars and their pins
sadly i dont see this happening, and the infection was probably from ultra-unhygenic gym practices (my gym owner rarely, rarely cleans anything, but he does vaccuum) rather than any insidious breakout of the bug, so use common sense, use a towel, maybe some gloves, and wash your hands
cheers