The proposed study introduces a joint optimal control strategy for automated bus trajectories and signal priority to enhance transit corridor reliability, where the operations of multiple bus lines are hindered by differing control strategies. The optimization of bus acceleration maneuvers and signal priority schemes is performed concurrently to minimize bus schedule deviations. The nonlinear optimization model is reformulated as a mixed-integer linear programming (MILP) problem and solved using a branch-and-bound solver, with an event-based re-computation scheme tailored for real-time operations. Sensitivity and computational efficiency analyses confirm the model's effectiveness under varying road geometries, signal parameters, and traffic conditions. Simulation results demonstrate that the proposed model improves bus punctuality by 57.2%, with only a 3.7% increase in private vehicle delays compared to the trajectory control-only strategy. Furthermore, it reduces private vehicle delays by 14.7% compared to the signal priority-only strategy, while achieving similar reductions in bus schedule deviations.