Can you narrow down the date and location ? In the late Victorian era most circuses still had their brightly painted horse drawn wagons. Instead of using horses to pull them from town to town, they would be loaded on a string of flat cars. They would be loaded circus style, meaning the wagons would go up a ramp at the end of the track and slowly back up, towards the front of the train. Metal bridge plates between the flat cars let the wagon wheels roll from one flat car to another.
Circus horses and other domesticated animals rode in stock cars that traveled in the same train as the wagons. Exotic and dangerous animals were moved in cages that were built into often very elaborate wagons.
Depending on the size of the circus, if it was big enough, the performers and their costumes would ride in passenger cars that were pulled in a separate train. Smaller circuses could often get away with one train.
Source: "The Circus in America" by Charles Phillip Fox and Tom Parkinson. The third section of this book, "The wonderous one-day stand" will answer all of your questions about how a circus got into and out of town. This book has more colorful illustrations than the book I recommended two months ago. That book "The Circus moves by rail" has black and white photos that are more recent than the Victorian era.