If she works well in a curb, why not use a curb?
That said, about 3 months ago I started riding Mia with a bit sometimes. Sometimes she seemed to accept it fine, and sometimes she did not. The trend over time was downhill. I tried several different snaffles and a french link snaffle, and she worried more and more. The last ride, she spun herself out of control in the riding arena she's been in countless times. Diarrhea, rolling eyes, one leap & bolt for 3 laps of the arena...and having a bit in her mouth did NOTHING for control. I eventually got her to slow to a walk and I jumped off - after 2 hours of escalating fear. She bolted about 50' without me, then turned to see where I had gone. I walked over and removed the bit. She sighed and followed me with no sign of fear.
My point? Bits don't control a horse. Bits make our cues more subtle, but a scared horse won't calm down because of pain in the mouth. I tend to agree with those who say no one ever stopped a bolting horse...they just were on a horse that stopped bolting.
With Mia, things were bad enough that I stopped riding her and started her training over at square one. Round pen. Outside turns, inside turns, change to trot & canter and back down on verbal cues, coming in, coming in a little and stopping, backing...right now we're at trotting and cantering over poles. I was going to try riding her bitless in the round pen today but ran out of time, so tomorrow hopefully. We've done mounting and dismounts without problem on the left side, and are starting mounting from the right - that is scary for her right now. The poles are a baby step towards sacking out, which isn't so much about desensitizing as it is about teaching her to trust me in her fear.
She has holes in her training, and tack can't cure those holes. Training will. We did the same thing with Trooper last fall, and he's finally turning into a very willing and fun horse to ride.
Your horse doesn't have the severity of problems that Mia has shown, but you might consider starting her in a course of training while still riding her. I'm working with a trainer with Mia, but this book provides an outline of the training we will work thru:
Mia is back to riding bitless. She has gotten progressively worse with various bits, and I figure when things are going downhill, it is time to go back to the last successful stage. But until Mia learns to look to me in times of fear, she really isn't safe to ride even if I've been riding her for 2+ years. Happily, your horse is doing much better!
All of which is a long winded way of suggesting you 1) step back to what last worked well, and 2) that you run your horse thru a systematic training program to find & plug any holes. With Trooper, the process took 5 weeks. With Mia, we're still doing basic ground work after 4 weeks, and her stubbornness may end up taking 5 months instead of 5 weeks. Whatever. I've got a room full of tack, but my horse needs training, not tack.
And I apologize if my problems with Mia have made me look at all horse problems thru a single lens...I'm learning some stuff the hard way, and it tends to bias my thinking. Good luck & best wishes!