Mass Rapid Transit (MRT) systems, i.e. subway systems, all over the world, are experiencing an increase in ridership. This also means that in case of an unplanned MRT service disruption, the number of affected passengers is larger, requiring a fast and comprehensive response. In this paper, we thus study the disruption management of MRT systems. We develop an optimization model to identify the optimal bridging plan in response to an MRT disruption, so that the negative effects of a disruption could be minimized. Our approach supports deployment of multiple types of bridging buses, reflecting the diversity of vehicle types in a typical public transportation provider's vehicle fleet. The optimization objective of our approach is to decrease the travel delay of passengers and increase the number of passengers who can be served. We demonstrate the effectiveness of our approach on a hypothetical case study in the central business district of Singapore. Moreover, we validate our analytical results with microscopic simulation, showing that our simplified analytical optimization approach can be used for disruption response planning. Some deviations indicate, however, that a combined simulation and optimization approach yields better results to obtain an effective bridging plan.