Officials told sister station ABC 15 that no injuries were reported. The accident happened near Kingman, in northwest Arizona. Heavy rains pushed the bus down a wash when it flipped over.
Fire authorities said the people on board escaped through the windows waited on dry land for personnel to arrive. Responding personnel were stalled due to the significant rain causing other washes to be flowing.
"The occupants were extremely lucky to have survived the ordeal and were very fortunate to have no fatalities or injuries due to the remote location of the incident," Fire Chief Patrick Moore said in a statement.
Initial reports indicated there were 31 people on board; that number was later updated to 33. Officials say the bus may have been heading to or coming from the Grand Canyon Sky Walk, ABC 15 said. A rope team was called to the scene but was not needed.
ABC 15 and the Associated Press contributed to this report.