The need to reduce vehicle-related emissions in the great cities has led to a progressive electrification of urban mobility. For this reason, during the last decades, the powertrain adopted for urban buses has been gradually converted from conventional Internal Combustion Engine (ICE), diesel, or Compressed Natural Gas (CNG), to hybrid or pure electric. However, the complete electrification of Heavy-Duty Vehicles (HDVs) in the next years looks to be still challenging therefore, a more viable solution to decarbonize urban transport is the hybrid powertrain. In this context, the paper aims to assess, through numerical simulations, the benefits of a series hybrid-electric powertrain designed for an urban bus, in terms of energy consumption, and pollutants emissions. Particularly a Diesel engine, fueled with pure hydrogen, is considered as a range extender. The work is specifically focused on the design of the Energy Management Strategy (EMS) of the series-hybrid powertrain, by comparing the results achieved by different empirical or optimized approaches, namely Rule-Based (RB), Dynamic Programming (DP), and Pontryagin’s Minimum Principle (PMP). The simulation analyses have been carried out by a comprehensive model of the hybrid bus, that specifically accounts for performance, efficiency, and tailpipe NOx emissions of the H2 engine in a wide operating range. To this end, a model of the Selective Catalyst Reduction (SCR) system for NOx abatement, accounting for the exhaust thermal dynamics, is considered. This task is fundamental in the case of a series hybrid-electric powertrains that, depending on the EMS, may operate with long engine stops that negatively impact on SCR efficiency. The simulation analyses have been performed by considering three reference driving cycles for urban buses. In a further step, an Eco-driving (ED) algorithm was developed to optimize speed profiles, considering actual driving routes. Onboard cameras and GPS tracking devices were used to simulate Vehicle-to-Everything (V2X) data and to replicate real-world driving conditions. The full potential of Eco-driving is realized by treating the problem as a mathematical optimal control problem, with its solution derived through the application of Pontryagin's minimum principle.