Craigslist. You will want to find something that can at least resemble a period bike or an older one. Something with an inline or V-twin would work. 4 cylinders really did not become a ting until the 70's.
The good and bad thing about used motorcycles is that they often get left in peoples garages and sheds for years, and somehow people always loose the title. It sucks to jump through all the loopholes to get a new title issued; sometimes its not even possible. The good news is that, you never need to license a prop.
I'll bet if you put a add asking for a bike, someone will give one to you. Something like a Honda rebel could work well, its a twin, and its pretty light, making it easier to move around if you are not driving by running the engine.
Only times I have worked on ALL Shook up, were in open air venues, where a running bike was allowed. Whether or not you can use a running engine will be dependent on you specific building and local rules/laws.
Electric could be an option, I once helped
build build a 3/4ish scale 1932 Ford around a golf cart. I don't think converting a motorcycle to
electric would be particularly easy, but it is certainly possible. You could probably get buy with pushing the damn thing around, just
wire it up so the lights work. If I recall, the script does not really dictate that they drive around on it.