One person was flown to the Medical University of South Carolina hospital in Charleston, about 25 miles southeast of the crash, Highway Patrol Lance Cpl. Robert Beres said.
About 30 people were taken to area hospitals for treatment with mostly minor injuries, officials said.
"I didn't know what was going to happen," passenger Pamela Underwood told CBS News affiliate WCSC-TV. "You're like, 'Wow, is the bus going to stop?' That was mostly what I was thinking."
The bus, operated by 5-Star Transportation out of Bonneau, was headed from St. Stephen to Miami, Beres said.
"It was a freak accident, we don't know what happened," Charlie Hill, a co-owner of the bus company, told WIS-TV in Columbia.
An autopsy was scheduled Monday for the driver, George William Thomas, 58, said Perida Moultrie, deputy coroner for Dorchester County.
The wreck happened just after 1 a.m. on a rural stretch of the highway. No other vehicles were involved, Beres said. The wreck closed the highway for about four hours, but all lanes were open to traffic by 6 a.m., Beres said.
Hill told WCSC that approximately 50 passengers were aboard the bus.