They should always be in comfortable equipment. Then you need to train them to respond correctly, which is a process. If the horse does not respond correctly to something as inoffensive as a rope halter, there is no point in moving on to a bit. While the horse is in the rope halter and you are on the ground, you are also working on moving the hips, shoulders, backing, disengaging, flexing, going forward, stopping, etc. Once the horse is well trained and responding reliably, you then move to the saddle, and repeat all the same exercises while riding. Every exercise works on one thing at a time, and you don’t combine aids until the horse is proficient and reliable at the aids applied singularly. Sometimes when you combine aids, the horse stops responding correctly to one of the aids, and you have to go back and work on that aid by itself until he responds correctly again, then you combine.
If a horse has a “princess mouth,” you need to go back to the rope halter on the ground and get him broke 100% proficient on the ground, then get on with the rope halter and get him 100% proficient and then go to a bit. If Mr. Princess Mouth is not 100% broke in a rope halter on the ground you have a hole in your training, not a “princess mouth” horse.