By Lori Grannis

MISSOULA, Mont (Reuters) - Two people were killed and 33 others injured when a bus veered off an icy interstate highway in western Montana and rolled onto its side on Sunday, and police and hospital officials said.

Police said the death toll might rise. A spokeswoman at St. Patrick's Hospital in Missoula, where the most severely hurt were taken, initially listed two victims as critically injured, but one was later upgraded to serious condition.

The Rimrock Trailways bus, which had been traveling west on Interstate 90 from Billings en route to Missoula, was found on its side in the median, according to Montana Highway Patrol Sergeant Scott Hoffman. The crash occurred at about 7:05 a.m. local time.

"We had a bus traveling too fast for conditions," Hoffman said, adding that police were still investigating how precisely the driver lost control of the bus. No other vehicles were known to be involved, he said.

Hoffman said road conditions were slick and hazardous. "We were dealing with black ice," Hoffman told Reuters.

Some passengers were ejected from the bus, and three people, including the two who died, were pinned under the bus, Hoffman said. The driver survived and was among eight people initially listed in serious condition, he said.

St. Patrick's hospital spokesman JoAnn Hoven said 12 patients from the crash were brought there, including two flown to Missoula by helicopter. Four of those were treated and released and eight others were admitted.

Another 21 patients from the crash were taken to Community Medical Center in Missoula, five of whom were admitted for medical treatment of observation, hospital spokesman Geoff Peddicord said.

The only child reported injured in the wreck was listed as a minor among those at Community Medical Center.

Dan Ronan, a spokesman for the American Bus Association, a trade group that includes Rimrock among its members, said the driver was 53 years old with years of experience and a good safety record. He has worked for Rimrock for a year after coming over from Greyhound.

"He's very familiar with that route," Ronan said.

Electronic equipment on board the bus showed it was going 65 miles per hour, which is 10 miles per hour below the posted speed limit on that stretch of highway, Ronan said.

(Writing and additional reporting by Mary Wisniewski; Editing by Steve Gorman, Colleen Jenkins and Peter Bohan)