I've been sitting here, thinking back on the "bolting" behavior of my two present horses and what I've learned from/because of them. My worst case bolter is my half Clydesdale gelding, a huge, powerful horse with plenty of reasons from his past to want nothing to do with going away from home. He put me on the road to eventually understanding (or attempting to) the behavior. Bolting has been described as a "broken stop response." When you think about it, that's an understatement. So, riding around in a halter safely in an arena isn't really addressing the root problem. The person who brought to light for me, the fact that BOTH my horses had a "broken stop response" to a greater or lesser extent, was Larry Whitesell, a gaited horse trainer. He brings in lots of client horses with broken stop responses. His first steps are to walk with the horse in hand in the arena, giving the horse a signal to stop, then planting his feet. Nine times out of ten the horse will keep going, sometimes right through the bit. He says he's been dragged around the arena many times. Reinstalling the response involves doing this until the horse will stop at the slightest indication of the reins (NOT stopping because the trainer stops! And actually, not GOING because the trainer does, either...that is not teaching either response.) In my interpretation, I do an imitation of Parelli's four phases of cue firmness, giving the horse plenty of opportunity to stop when it feels me begin to take up contact on the rein, but having a "phase four" cue ready if the horse blows through all its opportunities to respond to a lighter cue. And then, the horse has to stay immobile while I keep walking a few steps after I've released the cue. It really works, it's a great test to see if your halter riding has got enough "meaning" for the horse to stop when you begin to pick up contact. Then of course you teach from the saddle, followed by teaching in an ever widening comfort zone.
The other thing I discovered is that it takes regular practice to keep the cues sharp. My little TWH mare is only mildly spoiled and can throw little tantrums, but she is the smartest little learner on the planet. (My half draft has a learning disability.) Still, she's very likely to say, "Well, I don't do stop cues on Tuesdays." And I must remind her how much fun stopping on cue she is missing!
So anyway, it might be a good test to see whether you need further work on rebuilding your stop response before heading out the arena gate.