When a group of autonomous surface vehicles (ASVs) sail from a wide waterway to a narrow waterway, one difficulty is to keep relative formation with collision avoidance. Scaling the formation sizes with formation shapes invariant is a promising way. This article investigates such a formation scaling control problem of ASVs with uncertainties and input saturation. A novel bearing-based adaptive neural formation scaling control scheme for ASVs is developed. The main idea of this formation scheme is as follows. Choose a small number of leader ASVs based on bearing rigidity theory and program their trajectories according to the kinematics of formation scaling maneuver. Steer remaining ASVs to follow leader ASVs via adaptive neural techniques and the formation sizes can be scaled only by leaders without redesigning control inputs of followers. To deal with the uncertainties of ASVs, weights updating of neural networks is simplified into one-parameter estimation in each control channel. Auxiliary systems are introduced for each ASV to reduce the effect of limited actuator capability. It is shown that desired formation scaling maneuver of ASVs can be achieved with the proposed formation scheme if the augmented formation is infinitesimally bearing rigid. Formation errors are guaranteed to be uniformly ultimately bounded. The main advantage of our scheme over existing results is that directional, computational, and actuator constraints are satisfied simultaneously in the formation scaling control of ASVs. Simulations and comparisons are provided to illustrate the effectiveness of theoretical results.