I used to be really nervous. My horse is a lovely boy, really easy to ride, and educated like yours, but I was heavy on his mouth and I would lean forward if he went faster than I wanted him to and he couldn't cope with that. It ended in me coming off badly and getting hurt, and I have struggled with confidence since. I used to feel sick at the prospect of riding.
What I did, was I put the equipment on my horse that I felt comfortable riding in. For me, that was a plain French link snaffle for flatting, and a kimblewick for jumping and hacking out, but it could be anything for you. Two rides in the kimblewick and I was feeling in control enough that I could concentrate on my responses to my horse being silly. I still ride in my kimblewick for jumping and I won't ride my horse cross-country without using the strongest rein setting, but I'm a different rider and we mostly have good rides now.
I do pop him over small jumps with his snaffle on now, which is something I just didn't do when I first put the kimblewick on. I haven't had a lesson since before I started using the kimblewick and though my coach gave me a lot of confidence I'm kind of dreading the day he sees the bit I use - he was dead against me bitting up!
IMO, use the equipment you feel like you have enough control in, and your confidence will improve. HOWEVER, I also think that you should do more round pen work in the snaffle working on stop. Stop means STOP NOW and if you don't get it, the horse needs to back up to the place where you first asked for the halt. With my boy, that can be anywhere from half a stride to halfway down the school, depending on how he's feeling, the speed we're going, and what bit I'm using. The important part is that I do demand the stop, and I do get it (regardless of how much force it takes - and a suggestion, don't use constant pressure, check and release), and that my horse backs up to the place where I originally asked for the halt.