This work presents a comprehensive investigation of the structural, magnetic, and electronic properties of the double perovskite Ba₂CoMoO₆ (BCMO). Single crystals were grown via floating-zone and Czochralski growth techniques and characterized using a set of complementary methods. X-ray diffraction analysis confirmed that BCMO crystallizes in a face-centered cubic (FCC) structure with space group Fm3̄m. Magnetic susceptibility measurements exhibit antiferromagnetic ordering below T_N = 20.1(1)~K. A spin-flop transition is observed at 26.5 kOe. Heat capacity measurements and entropy analysis are consistent with a J_eff = 1/2 ground state for Co²⁺ ions. X-ray absorption spectroscopy provided insight into the local electronic structure, revealing the spin-orbit and crystal field effects. The cluster-model analysis yields a g-factor of 4.36, consistent with a spin-orbit-entangled ground state. Surface photovoltage spectroscopy demonstrates a strong near surface optical response with an onset near 1.5 eV and a pronounced feature at 2.65 eV, consistent with visible range Co–O--Mo transitions in line with related Ba-based double perovskites, highlighting its potential for spintronic and energy conversion applications.