All right.
Most rodeo bucking horses are either geldings or mares. They have no testicles.
Bull riders ride steers as well as bulls. The steers buck just fine. Steers have no testicles either.
There are multiple references on this subject, including proper methods of putting on a flank strap, veterinary articles, and photographs. All of this is easily found.
There. You're standing there with your pants around your ankles, shoes four feet long, and a honking red nose, all because you have the kind of mind that cannot be bothered to actually find out if something is true or not before shooting your mouth off in absolute certainty of your rightness. I wish you were the only one.
Happy now?