I definitely think that hawkfish eat them. I don't ever see bristleworms in my reefs and I always have a hawkfish. Prior to adding them, I would occasionally see the bristles. But not afterward. I also think that wrasses (melanurus for sure) will eat these things. Triggers will eat pretty much anything, especially if they are hungry!
I do see the bristleworms in my refugium, where I do not have any fishes (for now). It'll be interesting to see what happens when I add a trigger or two to the fuge.