I'd go for a loose ring double jointed bit with an oval shaped piece in the middle. Stubben makes some nice ones. Her getting her head down isn't really about the bit though. She needs to push off her high end and work over her back to do that.
If u do just a snaffle make sure it's a 3piece not a 2 the screwdriver motion or what ever u want to call it can annoy ottb's or any Tbs mouth becuz of the low plate they have
Try a hackamore! They're amazing and if she doesn't like it, it's always good to have!
There's no special bit, you just need science. Just try a snaffle or something simple, maybe even bit less.
No bit is going to get her head down; she'll have to learn proper carriage and work it down herself. A simple snaffle, always smooth mouthed, in a single joint (make sure there's curve to the cannons), lozenge, or dogbone, along with training, is the answer for about 90% of horses. The other 10% would be bitless or in a different sort of snaffle, like a wide low hinged port or a low comfort port
I use a rubber d but you could also try a bitless bridle
I have my filly in a myler bit and my gelding in a hackamore
D ring Myler! Or a myler bit of any sorts. My OTTB mare loves hers. It is ported, so you don't get the tongue pressure, it also has a roller in the middle as she's quite fidgety and copper inlay aswell:). They are on the more expensive side, but they are 100% worth it!! Hope this hel
When you research what track life is like for a TB you will find they suffer through having their tongue tied down with a very uncomfortable bar bit . I highly highly suggest you try a copper bit nothing fancy or crazy looking, an simple D ring with copper rollers.
I trainer a OTTB and I used a 3 piece dog bone
I'd recommend going back to a snaffle and the work on the basics. Work on flexing, transitions, body control, push her into the bridle and keep moving forward to naturally establish collection and develop a stronger topline. Trot poles are a good exercise, so is flexing and counter flexing the head in circles or on lines, transitions and extensions, and moving the hips in and out down the rail.