What happens if I bump someone and they think there is damage to their car but I can't see any?

you should take pictures of the car that you think you have bumped to provide evidence to your insurance company.

And it always makes sense to call the police, even if there is no visible damage. Most insurance companies are going to need a report number to process an accident claim. That also gives you a reliable witness on the condition of the vehicles and the passengers at the time of the accident. If they do not stick around to meet with the police, it could result in a ticket to them for leaving the scene.