Basal melting of ice shelves is a major source of mass loss from the Antarctic Ice Sheet. In situ measurements of ice shelf basal melt rates are sparse, while the more extensive estimates from satellite altimetry require precise information about firn density and characteristics of near‐surface layers. We describe a novel method for estimating multidecadal basal melt rates using airborne ice penetrating radar data acquired during a 3‐year survey of the Ross Ice Shelf. These data revealed an ice column with distinct upper and lower units whose thicknesses change as ice flows from the grounding line toward the ice front. We interpret the lower unit as continental meteoric ice that has flowed across the grounding line and the upper unit as ice formed from snowfall onto the relatively flat ice shelf. We used the ice thickness difference and strain‐induced thickness change of the lower unit between the survey lines, combined with ice velocities, to derive basal melt rates averaged over one to six decades. Our results are similar to satellite laser altimetry estimates for the period 2003–2009, suggesting that the Ross Ice Shelf melt rates have been fairly stable for several decades. We identify five sites of elevated basal melt rates, in the range 0.5–2 m a$^{−1}$, near the ice shelf front. These hot spots indicate pathways into the sub‐ice‐shelf ocean cavity for warm seawater, likely a combination of summer‐warmed Antarctic Surface Water and modified Circumpolar Deep Water, and are potential areas of ice shelf weakening if the ocean warms.