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This paper presents structural, detailed magnetic, and exchange bias studies in polycrystalline Ba<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>ScRuO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>6</mn></msub></semantics></math></inline-formula> synthesized at ambient pressure. In contrast to its strontium analogue, this material crystallizes in a 6L hexagonal structure with space group P<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mn>3</mn><mo>¯</mo></mover></semantics></math></inline-formula>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 Ba<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>ScRuO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>6</mn></msub></semantics></math></inline-formula> develops antiferromagnetic ordering at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>N</mi></msub></semantics></math></inline-formula>≈ 9 K. Interestingly, below 9 K (T<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>N</mi></msub></semantics></math></inline-formula>), 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 Ba<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>ScRuO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>6</mn></msub></semantics></math></inline-formula> indicates that inhomogeneous hexagonal double perovskites are a promising class to explore new materials having potential applications in spintronics.