The Mardi Gras season here is starting which means beaded everything. Most either spot wash or hand wash. With multiple colors used hopefully they were prewashed before the design was applied and they are color fast. Forever New is the recommended detergent for most and what most of us use. Other than that protection is the key.
For a show shirt worn in an arena I would think using a powder brush (clean, scrupulously clean) to remove dust would work. A few I know use a blow dryer no heat setting to blow the dust off. To me that would just drive it further in but for them it works. Once all dust is removed then wipe with a damp cloth. Wear a thin absorbent shirt underneath to keep sweat off and use stain liners.
Some horse people change their horse, they change their tack and discipline, they change their instructor; they never change themselves.