The enhancement of surface diffusion (DS) over the bulk (DV) in metallic glasses (MGs) is well documented and likely to strongly influence the properties of glasses grown by vapor deposition. Here, we use classical molecular dynamics (MD) simulations to identify different factors influencing the enhancement of surface diffusion in MGs. MGs have a simple atomic structure and belong to the category of moderately fragile glasses that undergo pronounced slowdown of bulk dynamics with cooling close to the glass transition temperature (Tg). We observe that DS exhibits a much more moderate slowdown compared to DV when approaching Tg, and DS/DV at Tg varies by two orders of magnitude among the MGs investigated. We demonstrate that both the surface energy and the fraction of missing bonds for surface atoms show good correlation to DS/DV, implying that the loss of nearest neighbors at the surface directly translates into higher mobility, unlike the behavior of network-bonded and hydrogen-bonded organic glasses. Fragility, a measure of the slowdown of bulk dynamics close to Tg, also correlates to DS/DV, with more fragile systems having larger surface enhancement of mobility. The deviations observed in the fragility-DS/DV relationship are shown to be correlated to the extent of segregation or depletion of the mobile element at the surface. Finally, we explore the relationship between the diffusion pre-exponential factor (D0) and the activation energy (Q) and compare it to a ln(D0)-Q correlation previously established for bulk glasses, demonstrating similar correlations from MD as in the experiments and that the surface and bulk have very similar ln(D0)-Q correlations.