The simplest bitless bridle is a sidepull, which is generally a Western piece of tack. It is basically just a noseband, but constructed to be more stable than most halters. it doesn’t have any more “bite” than a leather halter.
There are also patented bitless bridles that have straps that exert pressure on the poll or jaw. I don’t like them because they don’t release promptly, meaning your aids are always going to be fuzzy and wont’ reward with a proper release.
Then there is the mechanical hackamore. This is in fact a very very strong bit, and can be made even stronger if you use a chain instead of a chinstrap. I rode with one as a teen, my horse was very light in it, but you can also cause a lot of pain with one.
Finally, there is the Western rawhide bosal, which is a specialist piece of equipment used in training the vaquero-style horse.
I’ve used the hackamore riding western as a teen, and a sidepull on my current horse, who is trained English.
If your horse is light to the aids, you can use a bitless bridle lightly. If your horse is pulling and running through your hands, you can also use a bitless bridle very harshly. You can pull a horse’s head right around just riding in a halter, if you need to or want to. And you can ride around balanced on the horse’s face, too. But then you can ride in a bit lightly, with very little contact, the way that good western riders do.
One thing you can’t do in a bitless bridle is ride on contact in any meaningful way. You just have to have a slightly slack rein. There is no real context for contact. Basically despite using an English saddle, you are riding “Western,” that is off the seat, weight, and leg. That’s fine, but it also limits some of what you can school.
