I have read some reports on cone snails regarded as its primary predator, but have not found any papers detailing specific predators of the bearded fireworm based on stomach contents, field observations etc.
All papers on predation and Hermodice seem to deal with predation on corals etc. by the worm. On the Feb 2010 coral-list you find 3 items on Fire-worm predators. Worm size is important and of course location since Hermodice also occurs in the Mediterranean.