Part of my job requires me to visit various parts of the office. I remember I was once walking around the building and walked upon some funk. I thought we had some kind of chemical spill...turns out it was the funk some guy's riding clothes. I smelled that jersey and shorts from like 30 ft away and my sense of smell isn't good.

Can you take the clothes in the shower with you and wash it with a bit of soap and then ring it out real good?

Maybe use Dr Bronners soap for shower and washing your riding clothes at the gym.