In the present study, we have obtained Bianchi type VI anisotropic model of the universe filled with a bulk viscous stress in the presence of variable gravitational and cosmological constants. Here we have assumed the cosmological term in the form Λ∝H to discuss the effect of cosmological variables. It is found that the bulk viscosity coefficient (ξ) is a decreasing function of time. The expression for proper distance, luminosity distance, angular diameter distance, look back time and distance modulus curve have been analyzed and also the distance modulus curve of derived model nearly matches with Supernova Ia (SN Ia) observations.