I ride my mare (4YO TB) on the trail in a rope indian hackamore. Mild, she likes it okay. Hoping to get a little-S soon.
She had a MAJOR freak out on the trail a couple weeks ago. I mean MAJOR. Out of her mind, shaking, afraid for her life. (Stupid ^$%@#*& cows!)
And even with just that little piece of rope across her nose, I was able to keep her from killing us.
Point being, if a horse isn't going to listen to you, it doesn't matter what is on their face or in their mouth. They will ignore you if they want. Lucky for me, my honest little mare was listening to me. (Though the ride still didn't end well; I made the mistake of getting off. She doesn't listen as well on the ground!
If your horse goes well bitless, try it on the trail. If they do better in a bit, use that. What matters is that the horse is paying attention to you.