Oh this is a LOVELY topic!
My first bitless ride came about with my last horse, Cisco. At the time is was about year after he had thrown me off and I was dealing with a lot of anxiety just sitting on his back. My inability to relax only added to his inability to relax and we were worrying each other in a really vicious cycle. He was nervous with my tension and I was scared to death he would buck again.
I had a friend come out to help me. A cowboy. I really wanted him to ride Cisco, push him a little and see if he would buck (then ride it out because he could - he does rodeo). Instead, he came and told me that he would help but that I had to do the riding. Part of my tension was being played out by hanging on the reins. Since Cisco was in a snaffle, that meant I was hanging on his mouth constantly. My friend produced a western side pull and asked me to use it, and then in the follow few weeks I had a few riding sessions with him where he taught me to stop relying on the reins for balance, sit up and back (and he gave me pointers for how to sit a buck if it happened again
). From then on, Cisco was only in a bit for a short period of time after that (a few days about six months later during a clinic). Then I bought a cross under style of bridle (not a Dr. Cook but similar, and made locally of nice english bridle leather....it was a lovely bridle) and from that point on he was never in a bit again. He was more relaxed, but I was more relaxed. He was better balanced, but I too was better balanced. I began to learn more about the magic of lateral work as well...so really, I don't know how much was the lack of a bit. So much changed within ME at that time that I don't know what really changed his life. Being bitless was part of it, certainly (because my cowboy friend was convinced that I was causing him some claustrophobia), but it wasn't the only thing that changed. Everything changed. That was all around the time I also started working with a cordeo, and doing more and more play on the ground.
When Tam came along, I promised him he would never be in a bit. He has never tasted metal in his mouth.
For safety and control, we worked on halt so much that it became very solid. I also, by that time knew more about the relaxation of the horse and both Tam and Cisco became very soft and "bendy". So I knew if something went wrong all I had to do was ask for a bend in the neck (like a one rein stop) and I could carry that through to disengaging the hindquarters when needed.
I also learned to ensure my lateral work (even a simple leg yield) was really solid...so if I am riding and Tam gets too excited, rather than relying on restricting him with the reins (which I don't want to do) I can simply ask him for a shoulder in until he decides that's too much work and he will relax in a forward walk. Used that on a small trial ride once when we had to ride through the herd with a visiting stallion strange to the herd and the herd went nuts...so Tam got really worked up. Asking him to shoulder in, making sure I'm sitting in balance myself and correctly aiding, gets Tam to concentrate on the movement and he relaxes his body once again. On trail, I do not wish to have any contact at all, ideally, and I really just want him to maintain an even pace and keep his back relaxed. If he tenses, I lightly pick up the reins and ask for shoulder in or leg yield along the trail. I do this carefully so that the movement is done with his atlas open in the appropriate direction and there isn't too much bend in the neck. He has to relax the atlas to do it, which relates to a relaxation in the rest of the body.
In the arena, if a little tension creeps into his poll, I ask for very tiny atlas flexions for several steps left, then several steps right, so he's effectively changing band on a subtle level down the length of the arena without going into a full shoulder in. He relaxes the poll again.
There are folks out there of course that say that mobility of the jaw, via a bit, is a necessary component to the decontraction of a horse (in the classical tradition). That if there is no bit, you cannot have the jaw mobility (the soft, relaxed chewing of the bit). I cannot prove but do contend that the key is in the poll/atlas and not in the jaw, and if one has the exercises in place to ensure the relaxation and willingness of the horse to maintain a freedom in the atlas, then the jaw can be bypassed. Beside, Tam does loads of chewing while I'm riding...there just happens to be a cookie in his mouth quite frequently rather than a bit.
I would like to say however...that I ride with friends who use bits and those friends have lovely hands, lovely balance, relaxed and happy horses and we are all travelling the same road of learning. Some with bits, some without. But to them, composure and relaxation (or relaxed energy which allows for nice engagement and willingness from the horse) are every bit as important as they are to me.
I've been very lucky to find some very knowledgeable people, who all ride with bits, that are willing to share with me what they know and who keep a very open mind about the outcome. They want me to succeed. Some from curiosity to see where I'll get with Tam, and others who are simply sharing because they love to share.