Yes, and yes. Yes.
I supposed you're so excited to do this, that you didn't even remember to ask how to find one of these fine pieces of entertainment. So, I'll assume that you asked the question.
There is several ways, you can look in your local paper. When rodeos come into town they advertise so they can get people to come in and pay to watch. People that go to rodeos also listen to Country and Western, so listen to your local C&W station.
You're going to need the proper clothes for this adventure of yours, so when you go to your local western store to get your drugstore cowboy on ask the clerk there, and unless they're a fellow drugstore cowboy they should have some information on upcoming rodeos and local places you can take a bull for a ride. Tell them you're looking for somewhere you can ride as an amateur, preferably in the amateur circuit, as I don't think you wanna "kick the bucket" on a stud bull in front of 10,000 people.
As well, if you have any Indian Reservations near by, you can see if you can get in on their amateur circuits.