Well what does your coach and trainer tell you to do?
Let's say you are making a left turn around the barrel.
--Make sure you are not cutting into the pocket at the start of your turn. If you do that, your horse will be forced to come out of the turn wide in order to avoid knocking the barrel over. I personally like Charmayne James method where you stay the same distance from the barrel all the way around (not a V shape and not a rollback type), but this will vary from trainer to trainer and will vary based on the horse's style.
--What you doing with your legs, hands, body, eyes, when he does this? If you are "ending the barrel early" by looking at the next barrel too soon with your eyes, your body language could be inadvertantly allowing him to drift. Make sure you finish the barrel completely before you focus on the next one.
--When he starts to drift, make him circle the barrel a few times. Teach him to wait for your cues and listen to them. Use your outside leg on him to keep him in his turn. Therefore, he should be sensitive to your leg cues as legs are really important for control in the turn, moreso (I believe) than your reins.
It's hard to say exactly what's going on without seeing a video of the problem. I am only speculating at this point, trying to guess what might be going on.
Dena Kirkpatrick has a lot of videos on YouTube. I suggest you watch them. Here is one of them that may go over something you are missing in your turns.
Sherry Cervi also has a few videos. On this particular video, at about 1:20 into the video she specifically mentions something about drifting at the end of the turn.
As far as the bit goes, either a different bit may work better for him or he's just "acting up" with it by resisting. When you ask him to give to the bit, he should do so with no questions asked. If he does not, you've got to go back to some training basics, which I would hope your trainer and coach would be able to help you with.
This is nice little segment that Dena Kirkpatrick has on bits she likes.