I looked at your pic...yes that is definitely a bristle worm. They aren't all bad. There are many species that look very similar.
In my experience, the one's that eat coral tend to be very "not shy" about crawling around. In order to eat a coral, they have to latch on and gum/scrape it for a loooong time. So it should be easy to catch one in the act. If you want to get rid of him, it is as easy as picking him up with tweezers. Don't handle them with your hands.
I say all this because you should not just go catching every one you see. Try to catch the bad ones and leave the good ones. The good ones are quite useful clean up crew members.
