The incident happened Sunday afternoon outside Kingman, Ariz., when the bus encountered heavy rains and flash floods, The Arizona Republic reported.
"The bus driver attempted to cross a wash. The bus stalled. Then it started to float down the stream 300 yards," said Patrick Moore, fire chief of the Northern Arizona Consolidated Fire District.
The driver maneuvered the bus into a tree, but then a second current smashed into the bus, causing it to flip over.
All 33 passengers managed to escape, Moore said.
"The occupants waited on the dry land for personnel to arrive. Responding personnel were hampered to reach the scene due to the significant rain causing other washes to be flowing," Moore said. "It's astonishing that no one was hurt or injured because it had the makings of a terrible tragedy."