Do you have a small outdoor paddock? Is your horse ok with bareback stuff? I would just get on in the turnout and see if they take advantage of the fact that you are on them without any tack. That's all I really did. I mean it's not so much the teaching them to respond that we don't get the concept of right? It's the whole are you going to act like an idiot if I have no way to stop you thing that makes everyone nervous about taking off the tack. What's your horses personality? I've only ridden two horses bridleless, my mare who I have had from birth, so there's a foundation for you, and another who just choose to show her talent in going bridleless, another mare, I'm noticing a theme here. Are mare's more predisposed to going bridleless? Anyways, if your horse is not going to act stupid in a small paddock, try moving into a ring and seeing how much he/she will respond to just leg aids. My mare is a bit dull, so I think she is happy to just poke around, but her training did allow for me to kick her into a canter and hold her against the rail. I can sometimes change direction, and she is very understanding of the situation.
Hold up, I've ridden three horses bridleless, the bridle truly broke while I was out schooling and I somehow managed to keep a galloping horse in the ring and steer around jumps until a woman noticed me and closed the gate to the ring, but that was on accident. No seriously, not using this story to brag, the ground just didn't look that fun that day, but that is the level of calm I can possess even in an out of control situation, and how well I can get a horse to leg yeild, though I had a saddle then so I literally threw my weight to certain sides to avoid careening into jumps.
Back to the original topic, if it's just a matter of getting over the initial fear of not having any tack, do it in a small space and see how your horse reacts. Also, I don't consider riding without a bit as tricky as some people make it out to be, I switch regularly between having a hackamore or a bit depending on how much lift I want over the pole, it makes not difference to me other than as a tool/leverage if they have a bit in their mouth, I really don't think of it as a disadvantage, but I recommend it if you haven't tried, starting there perhaps? Hope this helps, you said you wanted more detailed instructions, and though I can't tell you the best way, I can tell you how i accomplished what I did.
Troubled TB ~"A thorn by any other name will prick just as deep." @-'--,---