The accident happened near Canon City, southwest of Denver, as the bus of Texas students were returning from a ski trip, reports Correspondent Eric Singer of CBS affiliate KKTV-TV.
The bus, carrying 57 people, spun before it left the road and rolled at least three times before stopping in a gully 100 to 150 feet away, Canon City Police Chief Martin Stefanic said.
One of the passengers, Casey Dubbelde, said the bus was carrying mostly high school students from Houston on their way back from the Crested Butte resort in western Colorado.
"The bus started to rock and started to turn to the right and went off the right side of the road," he said. "I woke up in the dirt. I assume I fell out a window."
Fire Capt. Dave Boden said it had been snowing in the area earlier Tuesday, and the highway was icy.
Of those on the bus, only four were adults, State Patrol spokesman Ron Loven said. He said the others, generally between the ages of 14 and 18, were on a trip at least partially arranged by Windwood Presbyterian Church and Bethel Independent Presbyterian Church, both in the Houston area.