sounds like you got a case of the amphipods or copepods. They are fine for the tank and infact show that your tank i a healthy enviorment.
I know bristle worms are bad
I never felt they where bad. They are great detravores in that they clean up fish waste, uneaten food, and dead and decaying items from the tank. If the anenome was dieing or dead the worms would have been doing what they do naturally. Eat dead or decaying material.
Personally I would not blam 'common' bristleworm on the anenome dieng. Anenomes seldom do well in a tank and often die of starvation due to lack of food and/or poor light conditions.