In general aviation there isn't really a yes/no definition. It's a judgement call. As a newbie, and the owner of a shared aircraft, it's prudent to err on the side of caution and report anything more than minor bounces.
If it made you worry that you damaged it, it's hard enough to let someone know. Especially if the nose gear came down hard, or worse, first, the nose gear being the more delicate element.
Golden rule: You get in way less trouble with other shareholder partners and the person maintaining the airplane by reporting non-damage than by not reporting damage. You may find that you'll report something, they'll ask you to describe it in detail, and they may just say don't worry about it.
Or, you tell someone you had a bad bounce, they'll go out and give it a once over by eyeball, and if the thing looks like nothing's changed, like one wing tip a little low to the ground, that'll be it. Or they may start pulling cowlings and access panels, but you've covered your behind.
In any case, you'll get brownie points as someone they can trust not to hide your embarrassments (because it's the people that hide that stuff that other pilots fear the most).
The benefit is you can then observe the result if the airplane gets checked over and a thumbs up/thumbs down given, and you added some new data to your internal knowledge and experience database that helps you next time decide what to report and what not to.
As far as the airplane is concerned, all that matters is, is something permanently bent, or worse, fractured/cracked/torn. If nothing's bent out of its original shape, it's fine. The weak points are the gear leg roots and the socket structure the gear leg plugs into for cantilever gear (of the equivalent points at the fuselage for a strut based main gear), and the nose gear's attachments to the firewall or engine mount.
The decision to ground yourself if you landed really hard at some outlying airport is a little harder. If that was the case, I would inspect the airplane myself and stand back and look at it to see if everything was normal and if nothing stood out I'd fly back, but I'd still report the event.
Everybody bounces their airplanes, and over time you'll learn what's worth bothering with, and what's not.