The Colorado State Patrol said the bus came to rest after rolling on its side along Highway 114 west of Gunnison.
The injured include an 11-year-old girl in serious condition, Colorado Springs' KOAA-TV reported. The others sustained minor injuries.
The bus was carrying 46 members of the Trinity United Methodist Church congregation, ages 5-71, from Denton, Texas. The group was on its way to Crested Butte on a Gotta Go Express Trail Ways bus driven by Fred Korenegay, 47, the TV station said.