When a bus on a scheduled trip breaks down, one or more buses need to be rescheduled to serve the customers on that trip with minimum operating and delay costs. The problem of reassigning buses in real-time to this cut trip, as well as to other scheduled trips with given starting and ending times, is referred to as the bus rescheduling problem (BRP). This paper considers modeling, algorithmic, and computational aspects of the single-depot BRP. The paper develops the sequential and parallel auction algorithm to solve the BRP. Computational results show that our approach solves the problem quickly.