Your post actually inspired me to join the forum board, I wanted to share my experience with my bitless bridle.
I have one (actually 2) of the Nurtural bridles (the first one got replaced after a rein got stepped on and the cheekpiece snapped, but hey, no mouth injuries!). It is a Canadian made cross-under style bridle. (Nurtural Bitless Bridle – The better bitless bridle
) I started using it on my baby when we started riding and have never gone back. She carries a bit comfortably and was ridden consistently in one when I leased her out for a year, but I honestly feel like I have more 'control' with the Nurtural. All I do is trail ride and I have never been in a situation where I was unable to guide her with it.
I would have to say that introducing one is like using any other piece of equipment - slow and steady. The biggest difference I think is the squeezing sensation from the cross-under, some horses do well, some do not tolerate it. I would just attach a lead rope to the rein rings and lead your horse around for a bit to get used to it. Otherwise, direct reining works just as usual.
As for gaited horses - The place I board at now, the gal rides all her horses bitless, some cross-unders, some sidepulls, whatever the horse was more comfortable with. 2 of them are Tennessee Walkers, 2 are Missouri Fox-trotters. None of them seem to have had their gaits affected by being ridden bitless.
Sorry, you got a bit of a novel in return . . . post if you have more questions!