  We present results for the O(alpha_s) virtual corrections to q g -> W b bbar
q' obtained with a new automatized approach to the evaluation of one-loop
amplitudes in terms of Feynman diagrams. Together with the O(alpha_s)
corrections to q q' -> W b bbar g, which can be obtained from our results by
crossing symmetry, this represents the bulk of the next-to-leading order
virtual QCD corrections to W b bbar + j and W b + j hadronic production,
calculated in a fixed-flavor scheme with four light flavors. Furthermore, these
corrections represent a well defined and independent subset of the 1-loop
amplitudes needed for the NNLO calculation of W b bbar. Our approach was tested
against several existing results for NLO amplitudes including selected
O(alpha_s) one-loop corrections to W + 3 j hadronic production. We discuss the
efficiency of our method both with respect to evaluation time and numerical
stability.
