A small pickup truck then rammed the bus, but the driver of the truck was uninjured, said DPS spokesman Tom Vinger.
The bus left Monterrey on Tuesday about 7:30 p.m., Vinger said.
"The investigation is centering on driver fatigue," he said. "It looks like he ran off the road, overcorrected, then tipped over on the passenger side."
Vinger said a key aspect of the investigation is how long the driver, identified by the bus company owner as Roberto Cruz, had been behind the wheel and whether any state or federal restrictions on hours driven were violated. Cruz, 42, was not seriously injured, Vinger said.
Capricorn Bus Lines Inc., which owns the bus, said there was only one driver aboard.
Vinger said the bus was under lease to International Charter Services Inc., also of Houston.
"At this point, and I want to stress it's extremely early in the investigation, but everything appears to be in order both for operating authority and driver's license requirements," he said. Neither federal nor state officials could immediately say when the last time the bus was inspected.
Francisca Flores, manager of the family owned bus company, said it was the first wreck in Capricorn's nine years. She said the bus carried 47 people, including the driver.
Flores said the company has four buses and only makes trips between Houston and Monterrey. She referred other questions about Capricorn's operations to a company representative who wasn't available.
A woman who answered the phone at a number listed for International Charter Services hung up when called twice by The Associated Press.
Capricorn is registered as an "intrastate" operator and is not subject to federal regulations, said Melissa Mazzella-Delaney, a spokeswoman for the Federal Motor Carrier Safety Administration.
International Charter Services is an interstate carrier, federal records show. Those records show it's had 103 inspections in the past two years, and its numbers for vehicle and driver violations are both below the national average.
Francisco Cardenas, 66, said he was asleep while returning from the holidays in Monterrey when he woke to the screams of people as the bus turned on its side.
"The hardest thing was to see all the other people," said Cardenas, who returned to Houston later Wednesday with a cut on his face and blood on his shirt and shoes. "There was no way out."
He said people eventually pushed the emergency exit on the roof to escape.
David Santos, 53, of Houston, said the bus wasn't speeding, but he felt the driver lose control then overcorrect. Santos said he saw one woman whose head was stuck under the bus.
The Victoria County Fire Marshal's Office identified the dead passenger as Pedro Mendez of Houston.
As of late Wednesday afternoon, 20 passengers were still hospitalized, including several in serious condition.
DeTar Healthcare System in Victoria, located about 125 miles southwest of Houston, took 22 passengers, said spokeswoman Judith Barefield. Of those, she said one had been transferred to another hospital outside Victoria for a higher level of treatment; two were in intensive care in serious but stable condition; one was in intensive care in stable condition; four were in stable condition; and 14 had been treated and released.
Another 24 people were brought to Citizens Medical Center in Victoria, said spokeswoman Shannon Spree. Of those, one was airlifted to Brooke Army Medical Center in San Antonio and two were airlifted to Wilford Hall Medical Center in San Antonio, she said. One of those airlifted had a severe head injury, she said.
Nine of the 24 were admitted to Citizens Medical Center, two in intensive care. One person had to have an arm amputated, Spree said. The other 12 were treated and released, Spree said. She said three or four of the passengers had broken backs and several had arm injuries, lacerations and orthopedic injuries such as broken collar bones.
San Antonio's University Hospital had received one patient in critical condition, said spokeswoman Dora Quiroga. Wilford Hall Medical Center spokeswoman Sue Campbell confirmed that two patients, both women, were transported there. She said they were out of surgery and in stable condition. One woman was at Brooke Army Medical Center in stable condition, said medical center spokesman Dewey Mitchell. Another person originally came to BAMC and was transferred to University Hospital, he said.
The south Texas crash was one of two in the U.S. on Wednesday. In Henderson, N.C., a Greyhound slammed into a tractor-trailer and plunged down an embankment. About 50 people were injured, officials said.
The bus was traveling from Richmond, Va., to Raleigh on U.S. 1 when a tractor-trailer ahead of it made a turn and the bus failed to slow down, said Sgt. Steve Green of the North Carolina Highway Patrol.