Well, you're wrong.
The solution is simply to use their magic a lot.
Basically the less you use magic (trying to hide, or 'useless' magic that nobody want you to use), the stronger the bite will be
Since Anna has been using her magic daily, she basically felt nothing
And since none of the Witches in hiding ever get to use up their magic power constantly, nobody arrived to this conclusion yet
Nightingale and a few Witches use their magic a lot, but they also try to reserve some power in case of emergency, so they still get the bite.