We consider the classic School Bus Routing Problem (SBRP) combined with alternate modes, where students are either picked up by a fleet of school buses subject to some constraints or transported by alternate transportation modes to a common destination (school). The constraints that are typically imposed for school buses are a maximum fleet size, a maximum walking distance to a pickup point and a maximum commute time for each student. This is a special case of the Vehicle Routing Problem (VRP) with a common destination. We propose a decomposition approach for solving this problem based on the existing notion of a shareability network, which has been used recently in the context of dynamic ridepooling problems. Furthermore, we build a connection between the weighted set covering problem and SBRP after decomposition via a shareability network. To scale this method to large-scale problem instances, we propose i) a node compression method of the shareability network based decomposition approach, and ii) heuristic-based edge compression techniques that works well in practice. We show that the compressed problem leads to an Integer Linear Programming (ILP) of reduced dimensionality that can be solved very efficiently using off-the-shelf ILP solvers. Numerical experiments on small-scale, large-scale and benchmark networks are used to evaluate the performance of our approach and compare it to existing large-scale SBRP solving techniques.