Perhaps look up the circus, and contact them? They should have a website. I would also research miniature horse breeders within an hour of your house. He may have come a long way.
If you cannot find the owners, and you decide to keep the foal, you need to get him gelded. Colts - a male foal - will grow up to be difficult to handle. They only ever think about mating, and can get very aggressive.
Bridles are used to ride horses. Since you will not be riding him, you will need a halter, sometimes called a headstall, and a lead rope. Until you know who he belongs to, I would not buy too much for him. Even though mini's are smaller than regular horses, they are just as expensive! You don't want to spend all that money on him only to have him taken back to his rightful owners.