Try the Bomber bits ultra comfy lockup
They make bits for tongue sensitive horses
I use a harmony snaffle with my chestnut mare. She loves it.
Nathe loose ring snaffle.
French link loose ring. I love this bit
I have a sensitive mare too and I rider her on a double broken leather covered snaffle.... big change vs the regular double broken snaffle!
happy mouthes are the way to go:)
A French link is probably your best bet for a sensitive mare. The extra joints make it more comfortable for the horse to carry in its mouth. A single jointed bit has a nutcracker type action on the tongue and the extra joint of a French link eliminates that.
I would say a loose ring snaffle, French link, or a hachamore depending on house sensitive she is. If she's a horse that likes to play with the bit then I would find one that has the rolling pin inside of it that the horse can play with while they have the bit in their mouth.
Maybe just a loose ring snaffle? Or a rubber bit. But be careful with the rubber bits because if they crack they're really unpleasant.
If she's extremely sensitive there are Mullen mouths that are simply rubber, so they bend and are very soft. There are also ones that are slightly harder rubbers but still have a bit of give. If you don't need something that extreme, you could try a simple rubber dee ring.
I like Nathe bits on horses with sensitive mouths my boy has got fleshy lips / tongue and he is going really well in a Nathe bit but he was really strong in other bits I am very impressed!
I have bought a happy mouth with a peanut for a sensitive mouth. Our new mare doesn't like contact and will throw her head up she's very forwarding going and keen to please and I dont want her to start evading the bit :)