Buildings are responsible for a significant fraction of the overall electrical load. Given the increasing penetration of renewables into the generation mix, it is important to make building loads flexible, to better match the variability in generation. Of course, building loads can be made arbitrarily flexible using sufficient stationary storage, but this comes at considerable cost. In this paper, we investigate how to reduce this cost by exploiting electric vehicle (EV) charging control for unidirectional and bidirectional charging. Specifically, we design a model-predictive control algorithm to reshape building load to match a specified load shape. In realistic settings and for two use cases, we investigate the degree to which the amount of stationary storage is reduced using EV charging control. In both cases, we find that our controller reduces the need for stationary storage compared to existing solutions. Moreover, bidirectional EV charging control substantially reduces the required amount of stationary storage.