Chimelong Safari Park without a car

Yes, you can drive your own car to enter the park, but you need to pay for it (CNY250 for each vehicle). You cannot get off the car and you can only tour around in the self-driving zone, so you may miss some spots, for which you can walk to see after touring around by car.

Personally, the most interesting part is in the Walking Zone, there are sightseeing buses and trams getting you around, that would be the best choice to cover all the fun stuff. You are even allowed to take pictures with the animals, feed them and get close to them.