This paper presents an exact approach for solving the simultaneous vehicle and crew scheduling problem in urban mass transit systems. We consider the single depot case with a homogeneous fleet of vehicles. This approach relies on a set partitioning formulation for the driver scheduling problem that incorporates side constraints for the bus itineraries. The proposed solution approach consists of a column generation process (only for the crew schedules) integrated into a branch-and-cut scheme. The side constraints on buses guarantee that an optimal vehicle assignment can be derived afterwards in polynomial time. A computational study shows that this approach outperforms the previous methods found in the literature for a set of randomly generated instances. A heuristic version of the solution approach is also proposed and tested on larger instances.