Recent advances in vehicle technology offer new opportunities for an electric, automated, modular bus (MB) unit with an adjustable capacity to be applied to transit systems, promising to tackle the resource allocation challenges of traditional buses in coping with uneven travel demand. Drawing on the concept of modular vehicles, this paper introduces a novel scheduling system in which MB units can be combined/separated from fulfilling imbalanced trip demands through capacity adjustments. We develop an optimization model for determining the optimal formation and trip sequence of MB units. In particular, given that the vehicles are electrically powered, battery range limits and charging plans are considered in the system scheduling process. A column-generation-based heuristic algorithm is designed to efficiently solve this model, with constraints related to travel demand and charging station capacity incorporated into the master problem and the trip sequence for modular units with limited energy solved by the subproblem. Taking real data from transit operations for numerical examples, the proposed model performs well in terms of both algorithmic performance and practical applications. The generated optimal MB dispatching scheme can significantly reduce the operating cost from $1534.31 to $1144.26, a decrease of approximately 25% compared to conventional electric buses. The sensitivity analysis on the MB dispatch cost and battery capacity provides some insights for both the scenario configuration and the battery selection for MB system implementation.