Start slow. I would begin with ground work. Getting your horse to trust you and figuring out your horse is very important, and if you really pay attention to your horse you can figure out how they react to those things. Mounted, I would you lots of seat and voice commands, that way you can tell your horse what to do without the bit. Make sure you are not nervous around the horse because that could be contributing. Hope this helps:)
Are you holding your reins tighter for the stop? Or just in general? I have my horses so they stop with my weight, voice and a little of my reins. I ride with a longer rein on mine because I know they are going to stop and because I ride mainly using leg pressure and my body weight not the reins.
You could try a softer bit? Keeli's a bit sensitive and she likes more of a consistent pull to slow down rather than jerking at her mouth,
Have you tried bitless? Depending on how sesnsitive he/she is, sometimes going bitless means you can have just the same presure on a sensitive horse than regularly