I agree, you do not teach a horse to go bridless. You work your cues away from the bridle to the leg only with the idea that the head is just an ornament. When you can get your horse solid without touching the reins for back up, you can slip it off.
I warn that you do not want to ride bridless too much though, as leg cues can get annoying and there is no real way to back them up. You want your leg cues to be quiet and light. Correcting with them alone can lead to tail swishing, head tossing, kicking and more.
Also, the longer the horse goes without being asked to lighten up through the bridle the heavier he will get. Legs to me, are secondary cues. Everything starts with softness in the bridle, leg is added, reins diminish, but remain the primary system if the legs fail.
Your horse could learn basic bridless riding in a matter of days, but to have self carriage and true control, you will have to spend a lot of hours in the bridle.