Public school administrators benefit from the ability to estimate future transportation needs on multi-year time scales, but student locations change from year to year. Continuous approximation (CA) methods are valuable for planning in similar settings where future spatial realizations of transportation demand are unknown. With this motivation in mind, this paper studies the use of CA methods for planar covering route problems, in which vehicles visit facilities (e.g., school bus stops, parcel lockers) that collectively ‘cover’ demand points (e.g., students’ homes, delivery recipients) within a certain radius. First, we show that typical approximations derived from the classical Beardwood-Halton-Hammersley Theorem do not necessarily produce appropriate route length estimates for covering route problems. We provide both empirical evidence and analytical results in support of our argument. Second, we leverage this analysis to develop an approach for strategic-level estimation of a school’s necessary school bus fleet size when exact student locations are unknown; this approach explicitly considers constraints on both physical bus capacity and the maximum duration of each bus route. We computationally validate our approach on a stylized planar region, then apply it to a semi-synthetic case study set in an actual school attendance region with a grid-like street network. Finally, we conduct an experiment on a highly irregular suburban street network to highlight the methodological limitations of using CA for covering routes in such settings.