Transport properties of graphene-superconductor junction have been studied extensively to understand the interplay of the relativistic Dirac quasiparticles and superconductivity. Though shot noise measurements in graphene have been performed to realize many theoretical predictions, both at zero magnetic field as well as quantum Hall (QH) regime, its junction with superconductor remain unexplored. Here, we have carried out the shot noise measurements in an edge contacted bilayer graphene-niobium superconductor junction at zero magnetic field as well as QH regime. At the Dirac point we have observed a Fano factor similar to 1/3 above the superconducting gap (Delta) and a transition to an enhanced Fano factor similar to 0.5 below the superconducting gap. By changing the carrier density we have found a continuous reduction of Fano factor for both types of carriers; however, the enhancement of Fano factor within the superconducting gap by a factor of similar to 1.5 is always preserved. The enhancement of shot noise is also observed in the QH regime, where the current is carried by the edge state, below the critical magnetic field and within the superconducting gap. These observations clearly demonstrate the enhanced charge transport at the graphene-superconductor interface.