this has been my personal quest for a long time since I have hyperhidrosis. what you want is a synthetic golf shirt. they can be expensive so keep your eye open for other similar shirts in men's sportswear. I like to also wear a liner of some kind - either white cotton or black base layer (wicking) more snug than the over shirt but not tight fitting and not a compression base layer. your basic exercise shirt material. check out a new balance outlet near you or a local Target store men's dept.

btw if a synthetic picks up your BO then it will rtequire a few washings - 1 washing isn't gonna do it. the liner I use also helps protect the overshirt from having this issue. you can toss undershirts when they get old

also - wash your riding clothes promptly after getting them wet ~ within 12 hours. lately I've been rinsing the underarms of my shirts when I get to work so they don't smell as they dry for the ride home. riding to work this time of year I wear just a single shirt (but always change into something fresh for work)