We present an implementation of the next-to-leading order hadronic production of a W boson in association with a pair of massive bottom quarks in the framework of POWHEG, a method to consistently interface NLO QCD calculations with shower Monte Carlo generators. The process has been implemented using the POWHEG BOX, an automated computer code that sistematically applies the POWHEG method to NLO QCD calculations. Spin correlations in the decay of the W boson into leptons have been taken into account using standard approximated techniques. We present phenomenological results for W b bbar-> l nu b bbar production, at both the Tevatron and the LHC, obtained by showering the POWHEG results with PYTHIA and HERWIG, and we discuss the outputs of the two different shower Monte Carlo programs.