I've never been over the border with a circus, but I can guess at some of the complications. First off, I'm going to assume that the circus is traveling together and it has animals. I'm going to further assume that the circus is from the US and is returning to the US.
Commercial carriers (and a circus would be a commercial carrier) are required to schedule their arrival at US customs (this is not a requirement for going into Canada). Upon arrival, the entire circus would be instructed to park and everybody exit the vehicles. You'd have some campers, some tractor-trailers, and I don't know what for vehicles.
The person in charge of the circus would go to the commercial desk for customs, with the appropriate paperwork (I'm not sure exactly what it would be). As soon as they figure out animals are involved, the person would be sent over to the vet, which is always in a different building.
The vet would then check each animal against its health certificate, looking at each and every one to make sure it is healthy and the appropriate animal. Ownership of the animals would be ascertained by the vet, and all wild animals would need documentation of origin. Once the animals are checked, the vet would then check the biohazards such as hay (I kid you not -- hay is a biohazard for customs).
Once the vet signs off, the guy in charge goes back to the main office. (By the way, vets only work during the day unless special arrangements are made and paid for.) There two or three agents will go out to inspect the trucks, looking in at least some of the compartments. Meanwhile the people would be being screened for appropriate paperwork. Since at least some of them would not be US citizens, this is going to take awhile.
Bottom line if you get through customs in less than four hours I'd be surprised, and I'd be expecting around eight. I've never made it over the border with a horse in less than four hours, unless it was my horse.
I would assume that a circus is more highly checked than most commercial traffic. That being said, the vehicles used have lots of hiding places. My guess is some one would be able to hide, but their nerves are going to be shot.
Also understand that crossing with animals involves some unusual considerations. For example, Highgate Springs, VT and Champlain, NY are very close together. Champlain is better for commercial vehicles, but Highgate is a lot better for animals. So a circus would go through Highgate even if it adds a hundred miles onto their route, because they'll have a lot more flexibility with Highgate.
ETA: I went back and reread the original post and realized you're going into Canada. That's a lot easier, but you still have the vet check. Biggest thing is you don't have to arrange a time and Canada is a lot more pleasant about it. However, for a circus, I'd arrange a time for crossing. Going into Canada I'd reduce the time down to a minimum of three hours and maximum of six.
Further ETA: This is a recent story out of Toronto --
http://www.thestar.com/news/article/897752--imported-horses-face-removal-or-death. A circus with animals is going to have a much different experience with customs than most people.
Best of luck,
Jim Clark-Dawe