Nail biting happens most often during times of stress. One estimate is that as many as 40% of all children over the age of six years bite their nails at some time or another, while as many as 20% of college students continue the habit. Although social pressures tend to limit thumb sucking, nail biting often continues into childhood and adulthood. There may be a family history of doing it, although it really is so common that no association with any specific factor of any significance has been found. Dental problems with alignment of an individual's bite and an increased incidence of infections of the cuticles are associated with nail biting.
So what do I suggest? Continue to be as positive and supportive as it sounds like you have been! Encouragement will go a long way in limiting this habit. Share the opportunity to pick a reward system that she thinks is "ideal" and keep giving her lots of positive reinforcement. I would definitely avoid any punishment, warnings, or making her feel ashamed. Of course, relieving any known underlying stress helps but will not do the trick alone. The use of something bitter on the nails only serves as a reminder for her that she's biting her nails, but tends not to work without the positive reinforcement. As you begin to work together in making this habit fade away, sometimes reinforcement from someone outside of the family, like her doctor or teacher, can help, too. I would also be sure to mention to the dentist at her next check up that she is a nail-biter. Good luck!