The electric vehicle contributes to reduce greenhouse gases emissions and get a greater integration of renewable energy. In this context, the implementation of urban buses implies the development of new grid infrastructures in order to carry out the electricity supply required by the charging stations. In order to optimize the size of these infrastructures and to have more power capacity, this contribution proposes the design and the sizing of a fast charging station with a stationary energy storage system (ESS) installed, to supply the energy of the buses that run on one of the lines of Pamplona (Spain). In this contribution, first, the power demanded by the charging point is measured at the fast charging station located at the Public University of Navarre. Second, three energy management strategies are developed with which to use ESS. Finally, the proposed energy management strategies are simulated with the measured data obtained. The results achieved in this contribution show that with a 40 kWh ESS, the power demanded from the grid can be reduced by a whole 70%, that is, from 250 kW to 74 kW. In addition, the power contracted in the electricity rate is reduced too. The authors would like to acknowledge the support of the European Union under the H2020 project STARDUST (774094), the Spanish State Research Agency (AEI) and FEDER-UE under grants DPI2016-80641-R, DPI2016-80642-R, PID2019-111262RB-I00 and PID2019-110956RB-I00, the Government of Navarra through research project 0011-1411-2018-000029 GERA and the Public University of Navarre under project ReBMS PJUPNA1904.