The bus skidded across a guard rail before sliding off U.S. 75 on the other side of a bridge over a creek. The right front tire of the bus carrying 55 people from Houston to Missouri blew out.
Investigators say the blown tire had been refitted with a new tread in violation of safety standards.
The National Transportation Safety Board also said late Friday that the driver was a 52-year-old who had a commercial license but whose medical certification had expired.
Authorities say the bus was operating illegally earlier in the day when the right front tire blew. The vehicle smashed into a guardrail and tipped over.
"There were people deceased from the front of the bus to the back of the bus," Officer Zachary Flores, one of the first on the scene, told The Dallas Morning News.
Workers were cleaning debris and gathering personal effects, including a blood-soaked pillow, a lone sandal, luggage and scattered pieces of clothing. There were blood spots on grass near where authorities had lined up six white body bags shortly after the accident.
The bus came to rest on its right side, partly on the northbound lane of the freeway and partly on grass. Workers righted the wreckage and loaded it onto a flatbed truck.
"Please pray for us," said Holly Nguyen, 38, a church member who was following behind the bus in a car but didn't see the wreck. She was anxiously waiting for word on whether her father, who was on the bus, was dead or injured.
Fire Chief Jeff Jones said 12 people died on the scene. Another two have died in hospitals. At least six more were hospitalized in critical condition.
"I saw crushing wounds," Jones said, "but there were very few walking wounded."
Investigators have interviewed the bus driver and he is in stable condition, Ayers said. Roads were dry at the time of the tragedy.
National Transportation Safety Board investigators were on the scene. Their investigation could take up to 18 months.
The accident happened less than a mile from the spot where a trucker crossed the median and killed 10 people five years ago.
The injured were rushed by road and air to several hospitals. Northbound traffic on the highway was shut down as ambulances and helicopters used the roadway and median to ferry the injured to hospitals.
Many of those on the bus were from the Vietnamese Martyrs Church of Houston and were on their way to a religious festival in Carthage, Mo.
Mary Nguyen, a member of the church for over 10 years, was at the church because she wanted to be near other parishioners after learning early Friday that a close friend had died.
Nguyen said she actually had planned to meet her friend, who canceled because of the trip. She began sobbing as she described the dream that kept waking her up, in which she was on a trip with the friend then opened a suitcase and saw dead bodies.
"I feel so sorry because she's dead ... she was just a very good person," she said. "The church is like one big family here. We're very close. We stick together."
Tinh Trinh, a church member for 20 years, said he was waiting to hear how one of his wife's friends was doing.
"I myself cried this morning when I heard the news," said Trinh, one of only a few people at the large brick church early Friday.
The Marian Days pilgrimage, which started in the late 1970s in southwest Missouri, attracts thousands of Catholic Vietnamese Americans each year. Many attend a large outdoor mass each day while enjoying entertainment and camping throughout the city at night.
The accident was the worst bus wreck in Texas since 23 people died when a bus carrying nursing home residents fleeing from Hurricane Rita was rocked by several explosions after catching fire on a gridlocked highway near Dallas.
Sherman is about 65 miles north of Dallas.