The crash happened at about 8.30pm yesterday (Saturday).
The 508 First Calderline bus from Halifax to Leeds Park Row is believed to have taken a wrong turn before it crashed into the rail bridge on Swinnow Road.
Pictures show the windscreen of the upper deck smashed on the ground.
An eyewitness believes there was just the driver and one passenger on board and neither person was injured in the crash.
Ricky Harris, who arrived at the scene shortly after the crash, said: "I arrived a few minutes after the incident. Thankfully there was only one passenger on board.
"I was talking to the neighbours and they said this accident happens yearly."
West Yorkshire Police were called to the scene and the bus was recovered.
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