Riding a horse bride-less is not something you train. It is the end result of good training and consistent cues by the rider.
If you can not move every inch of your horse with your legs and seat with a bit/bridle then you will not be able to teach them with out one.
There are many different ways to train a horse but no matter what or how you do it the end results should be a responsive well trained and light horse. Only then can you expect a horse to work without a bridle.
-I'm so busy... I don't know if I found a rope or lost my horse.
-An Armed Man is a Citizen an unarmed man is a subject.
-Where ever free speech is stifled Tyranny will reign.