The colors have been presented at rodeo and other horse riding events for decades with riders on horseback making a circuit around the arena and circling back to come to the center. The whole time keeping the colors in the proper order. Sometimes the the two color bearer riders are accompanied by unarmed guards on horseback. Other times it’s just the two color bearers. Either is fine.
The same thing goes for other unique colors presentations like a color guard on skates at a hockey game. This time, however, guards must accompany the colors per your service drill and ceremonies manual or, in the case of first responders, The Honor Guard Manual.
Carrying the colors out of order is inappropriate. As a guide, I created the above diagram to ensure proper carriage of the colors. The diagram below shows the color bearers turning on their respective initial sides and that puts the colors in the wrong position and must be avoided.