Quantifying the health effects of environmental exposures can require accounting for the spatial distribution of the exposure with respect to the individuals at risk. Prevailing approaches are focused on point source exposures, such as incinerators, but many environmental exposures are characterized by geometries not amenable to representation as a single point. We extend existing approaches to spatial exposure assessment to account for the risk posed by more complex potential environmental sources, such as waterways. We define a Bayesian nonparametric model of exposure whereby we partition the source’s spatial domain into non-overlapping subsets and model cumulative exposure for each spatial location as the sum over all subsets. Our model is a proper generative model of environmental exposure, which allows the model to account for uncertainty in the intensity of exposure at each point. The extension improves upon existing methodology by allowing for hotspot detection along the hazard, and a true accounting of cumulative exposure. We demonstrate our method on simulated data, and a dataset comprising reports of diarrheal illness in children in the Mezquital Valley, Mexico.