Probabilistic 1D inversions of airborne electromagnetic (AEM) surveys allow an exhaustive search of model space for each station, but they often assume that there is no spatial correlation between neighboring stations. This can result in abrupt transverse model discontinuities when attempting to construct a 3D model. In contrast to this, fully spatially regularized deterministic inversions can take spatial correlation between 1D models into account, but they do not explore the model space sufficiently to be able to evaluate model robustness. The Bayesian parametric bootstrap (BPB) approach that we developed is a practical compromise between computationally expensive exhaustive search techniques and computationally efficient deterministic inversions. Using a 1D kernel, we inverted for the interfaces, layer properties, and related uncertainties, taking lateral spatial correlations and additional prior information into account. Numerical examples revealed that a BPB technique was likely to explore the model space sufficiently for nonpathological situations. Using a subset of a large AEM survey collected in northwest Australia for aquifer mapping, we show how the BPB approach can be used to produce a spatially coherent map of the base of the Broome sandstone aquifer. The recovered uncertainties, which are likely to be one of the main sources of uncertainty in any groundwater model, exhibited the well-known increase in uncertainty of a depth to interface with increasing depth to the interface.