I think every cockatoo I have seen or known that enjoyed human company did exactly what you have described with the dance and head spin/snake type motion. I have never seen a wild one do the dance bounce you describe. I have seen one cockatoo in a wild flock do the dance bounce but he was formally a pet/companion bird that had escaped and somehow managed to be accepted by the local wild flock. This was at Greenvale Reservoir Park, I used to go there a lot with my mum and kids, my mum worked there for a while and I would walk the dog and kids in the park while she was working. They had magpies that would sit on taps waiting for my mum to start work, they would sit there till she turned the taps on for them to have a drink and shower.....it was cute to watch. There are quite a lot of birds there and the cockatoo that I mentioned caught my attention because he was comfortable with people and also spoke many words and phrases, he was so differently behaved to the rest of the flock but he was also allowed to hang out with them, I remember being fascinated by this as most pet birds are never accepted by wild birds.