  We calculate the production of a W boson and a single b jet to
next-to-leading order in QCD at the Fermilab Tevatron and the CERN Large Hadron
Collider. Both exclusive and inclusive cross sections are presented. We
separately consider the cross section for jets containing a single b quark and
jets containing a b-anti b pair. There are a wide variety of processes that
contribute, and it is necessary to include them all in order to have a complete
description at both colliders.
