Due to rush-hour effects, transient analysis may be necessary to model and optimize vehicle sharing systems. However, existing methods for transient modeling face computational challenges at scale. To solve this, we present trajectory-based iteration (TBI), a method for the efficient decomposed modeling of vehicle-sharing systems, and we extend it to a scalable method for non-convex, transient optimization problems. The proposed TBI method works by iteratively solving spatial submodels, then periodically updating the vehicle flows between submodels. We then present experimental results where our method results in a 37% improvement in runtime for solving fluid models for mobility systems. Then, we present a case study in which our optimization method results in an estimated 22% improvement in the objective function for a vehicle-sharing system with offline rebalancing.