  BaBiO$_3$ is a charged ordered Peierls-like perovskite well known for its
superconducting properties upon K or Pb doping. We present a study on the
transport and electronic properties of BaBiO$_3$ perovskite with strong
Bi-deficiency. We show that it is possible to synthesize BaBiO$_3$ thin layers
with Bi-vacancies above 8-10% by depositing an yttrium-stabilized zirconia
capping layer. By combining transport measurements with ab initio calculations
we propose an scenario where the Bi-vacancies give rise to the formation of
polarons and suggest that the electrical transport is dominated by the
migration of these polarons trapped at Bi$^{3+}$ sites. Our work shows that
cation vacancies engineering -- hardly explored to date -- appears as a
promising pathway to tune the electronic and functional properties of
perovskites.
