The morphology of glacier beds is a first-order control on their slip speeds and consequent rates of subglacial erosion. As such, constraining the range of bed shapes expected beneath glaciers will improve estimates of glacier slip speeds. To estimate the variability of subglacial bed morphology, we construct 10 high-resolution (10 cm) digital elevation models of proglacial areas near current glacier margins from point clouds produced through a combination of terrestrial laser scanning and photogrammetry techniques. The proglacial areas are located in the Swiss Alps and the Canadian Rockies and consist of predominantly debris-free bedrock of variable lithology (igneous, sedimentary, and metamorphic). We measure eight different spatial parameters intended to describe bed morphologies generated beneath glaciers. Using probability density functions, Bhattacharyya coefficients, principal component analysis, and Bayesian statistical models we investigate the significance of these spatial parameters. We find that the parameters span similar ranges, but the means and standard deviations of the parameter probability density functions are commonly distinct. These results indicate that glacier flow over bedrock may lead to a convergence toward a common bed morphology. However, distinct properties associated with each location prevent morphologies from being uniform.