A detailed description of the experience/ride with its "moving grandstands" can be found on the excellent NYWF64.com website, here.
The same website also reproduces Bradbury's text for the US Pavilion, here.
The same text would appear as an article entitled "Taming the American Wilderness" in The Daily Californian Weekly Magazine on 5 November 1968, but without any reference to the World's Fair.
It was the first of many Bradbury excursions into writing for events, exhibitions and rides, including some for Disney, the California Air and Space Museum, and IMAX Ridefilm.
On my recent trip to the Center for Ray Bradbury Studies in Indianapolis, I found Bradbury's scripts for all of these, including the New York World's Fair script: