Wy are you wanting to get rid of them? They are part of the natural clean up crew...
If they get large you can usually grab them with tongs when you put some food in the tank...
But if you are trying to get rid of the tiny ones there are some wrasses that eat them...
Yellow Corris Wrasse, Six Line Wrasse & Arrow Crabs are all known to eat BW's. But unless they are out of control, please leave em be. Great members of our CUC.
Sorry about your shrimp but I highly doubt the bristle worms are killing them. Once the shrimp dies the bristle worms are just doing their job of cleaning up the tank.
How are your water parameters? How are you acclimating the shrimp. Shrimp are very sensitive to s.g. And temperature changes and need a fair amount of time to acclimate to your tank water.
^ I agree it's not bristle worms. Are you sure your shrimp are not molting and you're removing them before they have had enough time to harden their new exoskeleton and still recuperating from the molt?
Bristle worm populations are dependent on the available food source (fish food), if you have too many worms you're feeding too much.
More than likely you either have a fish that likes the taste of shrimp, or they are not acclimating to your tank, whether its your process or its your actual tank...
Shrimp are one of the most finicky to acclimate....