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As the urban rail transit (URT) system plays an increasingly important role in supporting large cities' mobility around the world, service disruptions have become more prevalent, potentially resulting in severe economic losses and passenger safety issues. It is imperative to investigate effective response strategies to mitigate the effects of such disruptions. In response to URT service disruptions, this paper systematically investigates the bus bridging service design (BBSD) problem, which concerns the integration of bus bridging route design, frequency determination, and passenger assignment in the integrated URT and bus network. The problem is formulated as a path-based integer linear programming (ILP) model with the goal of simultaneously minimizing operator-oriented and passenger-oriented costs. A column generation-based approach is proposed to solve this model efficiently, allowing nonintuitive bus routes to be freely generated on the network dynamically. Our method has been tested with two different case studies based on real data from the Hong Kong Mass Transit Railway (MTR). Experiments demonstrate that our proposed approach can assist public transit (PT) operators in developing efficient emergency response plans for various potential disruption situations in advance. Even in the face of unexpected disruptions that necessitate a quick response, our approach can generate high-quality solutions in a matter of minutes. • A novel integrated model optimizes the bus bridging route design, frequency and passenger assignment simultaneously. • The trade-off between operator-oriented cost and passenger-oriented cost is considered. • The proposed column generation-based algorithm allows nonintuitive bus routes to be generated freely. • Extensive numerical experiments are carried out to seek valuable managerial insights for the public transit operators. [ABSTRACT FROM AUTHOR]