With urban rail transit (URT) systems playing an increasingly crucial role in megacity mobility, the rising frequency of service disruptions may pose substantial passenger delays and safety concerns. This emphasizes the need to prioritize resilience enhancements for the URT system. Bus bridging, an effective resilience-enhancing measure, faces challenges that effectively capture the unique features of bridging buses and stranded passengers, and rely on predetermined routes and fixed frequencies, diminishing service flexibility and efficiency in dynamic bridging environments. To overcome these challenges, we propose a novel approach using a multi-agent reinforcement learning model. This model treats bus bridging as a collaborative multi-agent task with the competition. Specifically, it enables bridging buses to adaptively select the next visiting station based on environmental characteristics. Furthermore, a competitive reward function is introduced to facilitate effective collaboration among all agents while preventing malicious competition. The case study results demonstrate that the proposed enhancing resilience method outperforms traditional reinforcement learning method and classic bus bridging strategy and can reduce the average waiting time and average travel time, especially in resource-limited and complex scenarios.