We present a comprehensive study of the electrical properties of bulk polycrystalline BiFe0.5Mn0.5O3, a double perovskite synthesized in high-pressure and high-temperature conditions. BiFe0.5Mn0.5O3 shows an antiferromagnetic character with TN = 288 K overlapped with an intrinsic antiferroelectricity due to the Bi(3+) stereochemical effect. Beyond this, the observation of a semiconductor-insulator transition at TP ≈ 140 K allows one to define three distinct temperature ranges with completely different electrical properties. For T > TN, electric transport follows an ordinary thermally activated Arrhenius behavior; the system behaves as a paramagnetic semiconductor. At intermediate temperatures (TP < T < TN), electric transport is best described by Mott's variable range hopping model with lowered dimensionality D = 1, stabilized by the magnetic ordering process and driven by the inhomogeneity of the sample on the B site of the perovskite. Finally, for T < TP, the material becomes a dielectric insulator, showing very unusual poling-induced soft ferroelectricity with high saturation polarization, similar to the parent compound BiFeO3. Under external electric poling, the system irreversibly evolves from antiferroelectric to polar arrangement.