I agree that "get off" is far cleaner and (for want of a more concise expression) better English but... and this is just a hunch of my own but "get off of" might be older than you think.
Norman French had a huge influence on how the English speak er, English.
"To get off" [insert Sid James gif here, if you like] in French is all one word "descendre".
So you'd say ''descendre du l'autobus" (I suppose they were probably getting off a horse back then but bear with me).
The thing is, I think it's that du (from) in the above sentence that's indirectly at work in this case. When French speakers (who would have been more dominant in certain parts of the country) moved towards speaking English for commercial and cultural (and not wanting to get your head chopped off) reasons, they would have been conditioned to placing an extra word in between "off" and "bus". "Off from the bus" just doesn't work, so they might have gone with "off of the bus" instead?
All this is just the theory of a man with a sick head on a Sunday morning. I'm no Suzie Dent and I could be entirely wrong but it makes sense in my tiny suffering little brain.
