Is the horse head shy at all? Other than refusing the bit? Can you halter it fine? And... when was the last time she had her teeth looked at?
Anyway, I personally would not be using a tom thumb, especially if your getting her to accept a bit. A tom thumb isnt the kindest bit. I would remove the bit from the bridle completely, and with her halter on, I would try and put it in her mouth. That way your not dealing with the whole bridle, and only working with her mouth. If she isnt accepting the bit, and she freaks, let her cool down, then try with some food on the bit. Say a fruit roll. Take a piece off, and let her smell it, then give the rest to her. Now take another one, and rap it around the bit, and ask for her to take the treat. Whatever you do, don't try and force her to accept the bit when she is all freaks out, that will result in making it worse.