  We study moduli spaces $M_X(r,c_1,c_2)$ parametrizing slope semistable vector
bundles of rank $r$ and fixed Chern classes $c_1, c_2$ on a ruled surface whose
base is a rational nodal curve. We show that under certain conditions, these
moduli spaces are irreducible, smooth and rational (when non-empty). We also
prove that they are non-empty in some cases.
  We show that for a rational ruled surface defined over real numbers, the
moduli space $M_X(r,c_1,c_2)$ is rational as a variety defined over $\mathbb
R$.
