"The driver said she heard a loud pop and then lost control of the vehicle," Vinger told The Associated Press.
The bus veered off the right side of the road before coming back across the interstate and into the median, where it landed on its passenger side, said Chuck Garris, emergency management coordinator for Atascosa County. The bus windows were shattered, and luggage, pillows and purses littered the median.
Garris said that when he arrived at the scene, stunned passengers with cuts on their heads and bruises were waiting for medical treatment. Most of the passengers were adults, although there were a few small children, he said. Garris said he believed a man and woman were killed.
"People were all sitting on the grass stunned, wondering what happened," Garris said. "It was a mess."
At least 30 people from the bus were taken to area hospitals, some with serious injuries, according to Vinger.
Garris said he believed around eight people were airlifted from the scene, and the rest were transported by ambulance.
Twenty-four passengers were in stable condition at South Texas Regional Medical Center in Atascosa County, hospital spokeswoman Danielle Flores said. One person taken there was later airlifted to a hospital in San Antonio, she said.
Two passengers were transported directly from the crash site to Brooke Army Medical Center in San Antonio, and at least four others were taken to University Hospital in San Antonio. Those patients' conditions were not immediately known.
Garris said he believed the driver helped remove passengers from the bus.
The bus was carrying Mexican and American passengers, Vinger said.
It was headed from San Antonio to Matamoros, Mexico, near the U.S. border, with a planned stop in Falfurrias, Texas. The bus was operated by Americanos USA, a wholly-owned subsidiary of Dallas-based Greyhound Lines Inc., said Bonnie Bastian, a spokeswoman for Greyhound's parent company, FirstGroup America.
"We are assisting local authorities with their investigation, and our top priorities are the passengers on board as well as our driver," she said.
Bastian said two buses have been dispatched to the accident scene from San Antonio to pick up uninjured passengers. One will take those who want to continue the trip to Mexico, and the other will carry those who want to return to San Antonio, she said.
Bastian said she did not have any information about the condition of the passengers or information about the driver.
"Right now our priority is to the passengers on the bus," Bastian said.
Americanos USA has a good federal safety record.
Before Tuesday, the company's vehicles were involved in 10 accidents in three states in the last 30 months, according to Federal Motor Carrier Safety Administration records. Tuesday's crash was the company's fifth involving injuries and second involving fatalities. One person died in a January 2009 crash in San Diego involving one of its vehicles. The company's driver was not cited.
With 137 motor coaches in service, Americanos has been involved in one accident for every 13 buses. By comparison, Greyhound has been involved in one accident for every eight buses.
In the last two years, inspectors placed Americanos USA vehicles out of service following 11.2 percent of their inspections, about half the national average of 22.3 percent. Inspectors placed the company's drivers out of service after only 1.8 percent of inspections, a far lower rate than the national average of 6.6 percent.
The National Transportation Safety Board probably won't launch an investigation, agency spokesman Keith Holloway said.
A spokeswoman with the Federal Motor Carrier Safety Administration said the agency had just heard about the crash and was beginning to gather information.