What's a good way to teach a child to ride a bike?

I am a nanny and am working with a set of parents who really think it's time their daughter ride her bike without training wheels. She's definitely physically ready and has good balance, etc., but doesn't really seem confident in herself and won't concentrate. If we stop taking her out she gets upset because then she can't get her brand new purple bike, but if we do take her out, she purposely wobbles the bike. We've tried talking to her and we hold onto the back of the seat while she rides. Are there any other tips you could offer? Nothing mean and nasty about pushing the kid--the parents have decided on this approach with the child (and the mom's a child psychologist so she knows what she's doing), I just need to take her outside every day and "practice" until she gets it... Any suggestions?