Mildest bit out there?

My trainer just got a thoroughbred mare about a month ago, and she is by far, the most sensitive horse i have ever ridden. All you have to do is think woah, and she stops, likewise with the upward transitions. The problem is, is that we cant figure out which bit she would go best in. We've tried a single joint D-ring snaffle and a hollow loose ring snaffle. So far, she goes best in the D-ring, because with the loose ring, she tosses her head, because the bars of the bit seem to be too big and a mouthful for her (she is about 16.1hh, but she has a real small head and mouth). Although she works fine in the D-ring, you can still barely touch her mouth. I'm going to try her in my single joint Happy Mouth D-ring tomorrow, but what I want to know is if there is another mild bit that I could try with her? I also have a mullen mouth Happy Mouth D-ring, a french link bit, and a full cheek happy mouth that I could try.