The bus was unlicensed, and authorities said a front tire that blew out had been illegally retreaded.
One of the survivors, Leha Nguyen, said she had started to doze off when she was awakened by a horrible noise, followed by screaming.
"I think I'm the luckiest one out of most people," said Nguyen, 45.
Twelve people died at the scene early Friday.
Three others died later, and the fourth, one of three people taken to Methodist Dallas Medical Center, died Friday evening, hospital spokeswoman Kathleen Beathard said Saturday. The hospital's other two victims, both men, remain in critical condition.
The vehicle was carrying 55 people from Houston to Carthage, Mo., for an annual festival honoring the Virgin Mary. Most of the passengers were from the Vietnamese Martyrs Church and two other mostly Vietnamese congregations in Houston.
The Marian Days pilgrimage, which started in the late 1970s, attracts thousands of Catholics of Vietnamese descent and includes a large outdoor Mass each day, entertainment and camping at night.
The vehicle's right front tire, which blew out, had been retreaded in violation of safety standards, said Debbie Hersman, a member of the National Transportation Safety Board. The tread had separated from the tire itself in a process called delamination.
"If there is a loss of pressure or the tire becomes delaminated, it's much more difficult to control the vehicle," she said.
It is legal to retread such tires but they may not be used on the wheels that steer a bus, Hersman said.
The 52-year-old driver had a commercial license but his medical certification had expired, she said. The driver was reported in stable condition at a hospital.
The bus operator, Iguala BusMex Inc. of Houston, had applied in June for a federal license to operate as a charter but was still awaiting approval, according to online records.
The company recently filed incorporation papers, listing the same owner and address as Angel Tours Inc., which was forced by federal regulators to take its vehicles out of interstate service June 23 after an unsatisfactory review, records show.
The review cited the company for problems in three areas: using a driver before receiving a pre-employment result, failing to require a driver to prepare a vehicle inspection report and using a driver who wasn't medically re-examined every two years.
Neither company is authorized to operate as a carrier in interstate commerce, said John H. Hill, administrator for the Federal Motor Carrier Safety Administration.
At a Houston building with a weathered Angel Tours plywood sign, a man declined to identify himself Friday or comment to The Associated Press about the wreck. An outgoing phone message at Angel Tours late Friday said the voicemail box was full.
It was the nation's deadliest bus crash since 2004, when 15 people were killed in a wreck in Arkansas on their way to Mississippi's casinos. In 2005, 23 people were killed near Dallas when a bus carrying nursing home residents away from Hurricane Rita caught fire in bumper-to-bumper traffic.
About 900 people gathered Friday night at Vietnamese Martyrs Church for a Mass attended by Cardinal Daniel N. DiNardo.
"We are here with them to pray for those who are lost and for God's consolation in this time of grief and loss," DiNardo said.
"The Vietnamese Catholic culture is very strong. A lot of those who have come here have been through a great deal just to get to this country. They've always preserved their Catholic faith. This is a trial. This is a challenge."
DiNardo said the losses, which include church leaders, are "incomprehensible."
One of the victims was identified as Hoangy Thi Dung, 71, of Houston, who was pronounced dead by a Grayson County justice of the peace. Sherman Police Lt. Bob Fair declined to release the names of the dead because some family members have not been notified.
Organizers of the festival in Missouri said the victims would be remembered at Mass and at various conferences during the gathering.