You didn't mention which camera, I have a Feiyu G4 for my gopro, it can work with similar cameras.
It doesn't stop bouncing altogether but is pretty good especially combined with silly walk technique.
For larger cameras a motorised gimbal won't be realistic for occasional amater use .
You can get simpler devices which work on a pendulum/inertia principal.
There are other tricks which are worth considering such as skateboards/scooters/bicycle. Sounds fun to try anyway.
Also something which hides camera movement is recording higher FPS and slow it down in post.
Obviously this isn't always suitable but in some cases it can work very well, and be barely noticeable or give a pleasing other-worldly feel e.g. flowing water