My daughter was a thumb sucker from the moment she was born. The dr. said she had sucked her thumb in the womb.
When she was around 18 months, we started trying to get her to stop. By two, she would not suck it unless she was tired or ready for bed. We tried the nasty stuff you paint on, wrapping it, and every other "remedy" recommended to us. Nothing worked. When she started seeing the dentist at 3, he said that her teeth were not damaged and that we would keep an eye on it.
Well, as she grew older, she would suck her thumb only when she was asleep. Even as old as 14 or 15, I would go in at night to kiss her goodnight after she was sleeping, and I would pull her thumb out of her mouth. If I told her the next morning that she was sucking it, she would deny it, because she was not doing it consciously.
Today, at age 30, as far as I know she no longer sucks her thumb. I don't know when she finally stopped. She has a beautiful smile and is a beautiful girl (not that I am at all prejudiced!). My advice would be to keep encouraging her and use the stuff you paint on, bribes, or whatever else is recommended. Let your dentist keep an eye on her, and as long as her teeth are okay, I wouldn't freak out about it. If she continues it in public as she gets older, her friends will probably tease her, which may help. Luckily, my daughter never sucked her thumb in public, so I don't know if the teasing would have helped her stop!