"The bus apparently failed to negotiate a curve, rolled off the road and onto its right side," Trooper Nate Reid told The Associated Press.
He described driving conditions as "bad," -- icy and snowpacked and the stretch of highway had several curves.
Reid said none of the eight people hospitalized had life-threatening injuries. Two were rushed to a Grand Junction hospital with serious injuries, while the other six were hospitalized in Gunnison with moderate injuries.
The other 38 people aboard the bus were taken by a school bus to a hospital in Gunnison, about 140 miles southwest of Denver.
"They were taken there for precautionary reasons; mainly bumps and bruises," Reid said. The patrol initially said all 38 had minor injuries.
The bus, operated by Gotta Go Express Trail Ways, was carrying a church group from Denton, Texas, to the town of Crested Butte.
Reid said the 38 were expected to continue their journey to Crested Butte, 40 miles north of Gunnison, after their hospital checkups.
He said he didn't have any more details on the church group.
A phone message left at the company's office in Fort Worth early Sunday morning was not immediately returned.
According to U.S. Department of Transportation records, the company operates 33 vehicles and employs 71 drivers. The company holds a "satisfactory" rating from USDOT and has reported only one crash with an injury in the last two years.