Food Grade Sodium hypochlorite decomposition/neutralization
Several good tap water rinses should probably get rid of any significant remaining amounts of bleach, although it's possible some bleach residues might adsorb to the wall of the barrel and resist these efforts.

Per here and here, if you want to be very sure the residues are removed, dissolve a handful of vitamin C (ascorbic acid) tablets in water and use that to rinse the barrels until all bleach odor is gone.  The ascorbic acid will act as a reducing agent and should reduce the bleach levels to next to nothing.

Dmitry is right: as an oxidizer, $\ce{H2O2}$ will probably do little to help.