  We analyse in a systematic way the (non-)compact four dimensional
Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl
structures with a Class A Bianchi metric have a conformal scalar curvature of
constant sign on the manifold. Moreover, we prove that most of them are
conformally Einstein or conformally K\"ahler ; in the non-exact Einstein-Weyl
case with a Bianchi metric of the type $VII_0, VIII$ or $IX$, we show that the
distance may be taken in a diagonal form and we obtain its explicit
4-parameters expression. This extends our previous analysis, limited to the
diagonal, K\"ahler Bianchi $IX$ case.
