having been a past nail biter myself... I can tell you, those bad tasting polishes don't work....
I have recently read that nail biting can be associated with Pica, which can occur in toddlers... (check out the net) it's when toddlers put things in their mouths that for most would taste awful.. for example , a child will eat paste or in some cases, the plaster off of the wall.... I have read that a child who might be lacking in certain vitamins and or minerals will seek out anything from paper to the tops of burnt matches. sounds odd, but it's true....
In addition, as someone who bit their nails for many years, I was in a VERY stressful environment as a young person and hence, would immediately bite my nails. it's also a learned habit (at least for some)....
is your daughter undergoing some stress, could be as simple as a new bed time or preschool? you just never know... but do try and notice when she resorts to it.. and see if at that moment you can gently speak with her and get her to tell you how she is feeling.. honestly, as a kid and young adult, I had such a habit of biting my nails that sometimes I was on auto-pilot..... I did it as easily as you automatically breathe... that's why it's important while she is young to try and help her become aware of it and see if you can replace it with something else.. like drawing..
Also, check out the net and see what it says about PICA , I found that VERY interesting... As a kid, I was not only a nail biter but would sometimes eat paper... the whole Pica thing has started to add up for me... I just wish I knew about it years ago... Oh and I no longer bite my nails :) I attribute that to less stress in my life and just trying to become more aware that I am doing it... also, better nutrition..
good luck to you and yours