While I haven't yet ditched the bridle entirely, I do use a neck rope from Linda Tellington Jones. I only do bridleless work in a round pen, and only use a saddle,with the reins in place where I can pick them up again as necessary.
A truly bareback and bridleless horse needs to be finely tuned to work off leg and seat pressure, the rider needs good balance and be able to communicate with their aids correct.
It's not something I'd advocate that just anyone goes out and does, particularly those with little experience. I haven't even gotten there myself and sometimes, I don't think I'd ever do it. I trust my horses immeasurably, but we're talking about a large animal with a mind of their own, and riding bareback and bridleless is taking a pretty big risk at times. (I might be more inclined to stick with riding bridleless but staying in a saddle. My Haflinger can be a slippery critter at times, and one small move in the wrong direction could be a problem)