Surface diffusion of molecular glasses is found to be orders of magnitude faster than bulk diffusion, with a stronger dependence on the molecular size and intermolecular interactions. In this study, we investigate the effect of variations in bulk dynamics on the surface diffusion of molecular glasses. Using the tobacco mosaic virus as a probe particle, we measure the surface diffusion on glasses of the same composition but with orders of magnitude of variations in bulk relaxation dynamics, produced by physical vapor deposition, physical aging, and liquid quenching. The bulk fictive temperatures of these glasses span over 35K, indicating 13 to 20 orders of magnitude changes in bulk relaxation times. However, the surface diffusion coefficients on these glasses are measured to be identical at two temperatures below the bulk glass transition temperature T_{g}. These results suggest that surface diffusion has no dependence on the bulk relaxation dynamics when measured below T_{g}.