In the arcade version of the game, the demo mode starts out with a picture of the Bad Dudes standing next to each other(not looking very bad yet) and a view of New York city in the background. after a few seconds, the following message is typed over the top of the screen:

Rampant ninja related crimes these days... Whitehouse is not the exception...

after another few seconds, the Bad Dudes strike a fighting stance (oooh... you can see they're bad now!), and the bad dudes title replaces the text at the top. Then the game proceeds to its teaser demo loop.

upon feeding the machine a quarter and starting a game, you are given a brief by some (military/secret service, i guess) guy:

President Ronnie has been kidnapped by the ninjas. Are you a bad enough dude to rescue Ronnie?

Oh hell yeah, you bet I'm a bad enough dude! I can raise both arms above my head and shout I'M BAD!!!