We calculate quantum transport for metal-graphene nanoribbon heterojunctions within the atomistic self-consistent Schrödinger/Poisson scheme. Attention is paid on both the chemical aspects of the interface bonding as well the one-dimensional electrostatics along the ribbon length. Band-bending and doping effects strongly influence the transport properties, giving rise to conductance asymmetries and a selective suppression of the subband formation. Junction electrostatics and p-type characteristics drive the conduction mechanism in the case of high-work-function Au, Pd, and Pt electrodes while contact resistance becomes dominant in the case of Al.