What sort of bitless bridle are you using?
If she's a broke horse--and it sounds like she is--it really shouldn't be a safety issue to take her out on trails at all. You can get her stopped no matter what, correct?
If you aren't already, you need to get more accustomed to cueing her with seat, leg, and to an extent vocal cues. For example, when I'm asking one of my horses to stop, the first thing I do is take my legs off them, sit deeply in the saddle, say whoa, and pull on the reins, in that order, and all in less than a second time span. But rarely do I have to pull on the reins because the horse is already transitioning to a halt. It's the same principle for any command.
I think perhaps you may be using your bit as a crutch, even though you aren't harsh with it. You may be less confident without its presence, and your nervousness causes your mare to be less responsive to the same subtle body cues you always give.
When riding bitless, pretend you are riding with a bit. Give the same seat cues. If she does not respond as she should, don't be afraid to tug on the bitless bridle in an appropriate manner, rewarding her compliance with a release, as usual. Teach her that it's the same sort of thing, and she must respect it and listen to you all the same.