We consider the finite horizon inventory routing problem with uncertain demand, where a supplier must deliver a particular commodity to its customers periodically, such that even under uncertain demand the customers do not stock out, e.g. supplying residential heating oil to customers. Current techniques that solve this problem with stochastic demand, robust or adaptive optimization do not scale to real-world data sizes, with the status quo being only able to perform inventory routing for ~100 customers. We propose a scalable approach to solving a robust and adaptive mixed integer optimization formulation that is made tractable with algorithms for generating worst-case demand vectors, heuristic route selection, warm starts and column generation. We demonstrate experimentally a mean reduction in stockouts of over 94% in our robust and adaptive formulations, translating to a cost savings of over 14%. We also show how to modify our model to achieve further cost savings through fleet size reduction. Our robust and adaptive formulations are tractable for ~6000 customers.