This paper presents structural, detailed magnetic, and exchange bias studies in polycrystalline Ba2ScRuO6 synthesized at ambient pressure. In contrast to its strontium analogue, this material crystallizes in a 6L hexagonal structure with space group P3¯m1. The Rietveld refinement using the room-temperature powder XRD pattern suggests a Ru-Sc disorder in the structure. The temperature variation of the DC electrical resistivity highlights a semiconducting behavior with the electron conduction corresponding to Mott’s 3D variable range hopping (VRH) model. The detailed magnetization measurements show that Ba2ScRuO6 develops antiferromagnetic ordering at TN≈ 9 K. Interestingly, below 9 K (TN), the field-cooled magnetic field variation (FC) of the magnetization curves highlights an exchange bias effect in the sample. The exchange bias field reaches a maximum value of 1.24 kOe at 2 K. The exchange bias effect below the magnetic ordering temperature can be attributed to the inhomogeneous magnetic correlations due to the disorder in the structure. Remarkably, the appearance of a large exchange bias field in Ba2ScRuO6 indicates that inhomogeneous hexagonal double perovskites are a promising class to explore new materials having potential applications in spintronics.