The multiferroic properties of (BCO) bulk and thin films are investigated for the first time using a microscopic model. The influence of ion doping on the multiferroic properties of BCO is also studied because the doping process changes the physical properties and can be used for potential applications in magnetoelectronic devices. The magnetization M increases by Mn and decreases by Ga‐ion doping whereas the Néel temperature decreases in both cases. There are some discrepancies by polarization whether it is ferroelectric or antiferroelectric. It is shown that bulk pure BCO is antiferroelectric because the electric field dependence of polarization P shows a double hysteresis loop and the dielectric constant has no anomalies at . In Ga‐, Mn‐ or Ti‐doped BCO a ferroelectric polarization appears. The specific heat shows a peak at for BCO. By Ga doping, this peak vanishes with increasing x. The multiferroic behavior of BCO is demonstrated in the magnetic field dependence of the dielectric constant. In BCO thin films, ferroelectric and ferromagnetic behavior is observed.