This paper presents the development of a control strategy for a fuel cell and supercapacitor hybrid power system for application in a city driving bus. This aims to utilise a stable fuel cell power output during normal operation whilst allowing variations to the power output based on the supercapacitor state-of-charge. This provides flexibility to the operation of the system, protection against over-charge and under-charge of the supercapacitor and gives flexibility to the sizing of the system components. The proposed control strategy has been evaluated using validated Simulink models against real-world operating data collected from a double-decker bus operating in London. It was demonstrated that the control strategy was capable of meeting the operating power demands of the bus and that a wide range of degrees of hybridisation are viable for achieving this. Comparison between the degree of hybridisation proposed in this study and those in operational fuel cell (FC) hybrid buses was carried out. It was found that the FC size requirement and FC variation can be significantly reduced through the use of the degree of hybridisation identified in this study.