When I first started to ride and learn about horses, tack and care etc, the only bitless option seemed to be a hackamore, typically the English hackamore. From what I remember thses were really nly used when there was a problem with a mouth, eg teeth or soft tissues. Back then teeth checks werent a matter of routine for most horse owners and really only if there was an obvious problem was the vet called in to check. It was just the way it was.
English hackamores are readily available and are fairly cheap to buy, you can often buy a secondhand one in good condition for a reasonable price.
Hackamores work by applying nose, chin and poll pressure when the reins are activated. There are other types including those with longer shanks (the metal part between bridle and reins) which give more poll pressure and the flower hackamore which allows various options. Ill put some links below.
I currently have a flower hackamore and did try that with Polly and Izzy too but I have to admit its not my favourite one, just personal preference and I would never rule it out for a horse if I thought they would suit.
Here is Polly trying the flower hackamore. I used my beta bridle for her and please note that the noseband is probably a hole or so higher than it could be but Polly seemed to prefer this arrangement. As you can see its quite adaptable, here the "shank" ring is at the bottom with the reins clipped on but you could turn it around and fasten the cheeks to it and clip onto one of the other rings. I did find that when used as above if the reins were used a little firmer that sometimes it would come outwards, I wasnt happy with this, it felt a bit clumsy. The other way i think would be much better but of course would have a different feel for the horse. This type of bridle seems to keep the cheeks in place, helping to prevent them getting to close to the eye and the beta nose helps to prevent it from slipping side to side.
Above are links to websites selling hackamores so you can see whats available, as you may see theres usualkly a lot of fluff and padding used to soften the effects and really to use them in a kind subtle way I feel you would need very little pressure on the reins.
Quite often people can attach the nose part to their ordinary bridle. The nose parts can be leather or beta biothane.