I use a KK training bit which is basically the bit that Hollybee showed you, I generally use plain metals but that's just because of what I am used to.
If you get nervous when he runs of and you clamp on or tense up he could think that you want him to run on.
Also, stopping when pressure is applied to the mouth is a trained response, so it could just be that he doesn't quite understand. Either way, letting him run on is not a good option.
Also, I don't know what you do generally, but just riding around an area that big isn't going to do much. Its just like riding out but in an enclosed space. I would work on 20 - 30 metre circles, with a lot of transitions. Start with the walk/halt ones and get it so that when you sit back, half halt and then give you cue for halt he stops, there shouldn't be pulling or fighting or running on. Get it going on the ground if he doesn't respond straight up. Then get into walk/trot and trot/halt, it is important that he learns to accept basic aids and the bit before continuing on to further training. Also, serpentines, little circles, lots of bending and flexing is good as well. This will get him supple as well as thinking.
Really consider changing the bit though. He doesn't need anything harsh and it can ruin a horse.