Gears Turning and Burning
A setup like the Ingo bike, kickbike/sidewalker/etc with an off-center front hub would do the trick. Replace the 'deck' with the exercise trampoline
I want to see what references I can find to The Bounce Bike
but search results are getting drowned out by some scooter share service at the moment.
I think the challenge would be in placing the deck/mini trampoline high enough that you weren't constantly bottoming out. Might also need slightly higher resistance coils to slightly reduce the bounce.