The top of the bus, carrying members of the Jehovah's Witnesses to a prayer meeting, was peeled back "like a can of sardines," The Miami Herald quoted a young passenger identified as Edwin Aparicio of Bogota as saying in Spanish.
The newspaper said the driver, Ramon Ferreiro, 47, who was not injured, made a wrong turn and entered the airport by mistake. He missed multiple yellow signs warning tall vehicles. The bus was 11 feet tall. The concrete overpass allowed just 8 1/2 feet of clearance.
"The last thing he should have done is to keep going," airport spokesman Greg Chin said. "That goes against all logic."
Killed were Serfin Castillo, 86, of Miami and Francisco Urana, 56, of Miami.
Thirty-one others were taken to hospitals, with three in critical condition. Three were later released.
The Herald said public records showed the bus belongs to Miami Bus Service Corp. of Miami, owned by Mayling and Alberto Hernandez. Mayling Hernandez told the newspaper passenger safety is her primary concern.
"At this time I'm worried about the driver and the families of the victims. I'm praying for them," she said. "My job is to worry about the safety of the passengers who are our clients. What we do requires a lot of responsibility. I didn't know the passengers but that doesn't mean I'm not suffering."
The company had no unsafe driving or controlled substances violations in the past two years, records indicated.