A great park.
There are two parts to the park- one in Botswana and one in South Africa. The Botswana side is the more undeveloped side. Contact DNPW in Gabarone for info. It is hard to get bookings for camping spots and you need to be self sufficient ie bring in your own water etc.
Most of the park is in South Africa. Roads are corrugated but OK. You really need a 4x4 or at least a car with good clearance. Certain roads are 4x4 only. There are 3 campsites, Twee Rivieren, Nossob and Mata Mata. they are quite big (full capacity perhaps 50 sites?) but no other option for camping.
No, there is no bush camping (any more than you can pull up by the roadside in Kruger and set up camp!).
There are also wilderness camps. These are not campsites but exclusive camps - usually with only 4 huts with their own waterhole. They are amazing but about 1000 rand a hut a night.
Go to the SAN Parks website and check out the KTP section - there is loads of info, a good map etc. Be warned there are very limited places in the park. Though it is huge it only has 1% of the bed/camping capacity of Kruger (because it has very limited water). The result is it is often fully booked for many months in advance. Also be aware of the size - for example it is not possible to drive between some camps within it in one day.
I hope you get to go - it is one of my favorite places.