i've made quite a few bows, but only chased the ring on a handful. What i do is this: I select my target ring, mark it with a sharpie, and then use the methods Pat B described to chase the ring ABOVE it. That way if i screw up a bit i'm still ok. Then when i get the entire back uncovered, down to one ring, i use a cabinet scraper to get down to the target ring. It's a safety.
I have a question: do you guys consider tool marks to be ring violations? Or is it only violated if you go through to the earlywood layer?