As an attractive alternative to the traditional plug-in charged electric vehicles (EVs), wireless-charged EVs have recently been in the spotlight. Opportunistically charged utilizing the wireless-charging infrastructure installed under the road at bus stops, an electric bus can have a smaller and lighter battery pack. In this paper, an improved opportunistic wireless-charging system (OWCS) for electric bus is introduced, which includes the opportunistic stationary wireless-charging system (OSWCS) and opportunistic hybrid wireless-charging system (OHWCS) consisting of stationary wireless-charging and dynamic wireless-charging. A general battery reduction model is established for the opportunistic wireless-charged electric bus (OWCEB). Two different battery-reduction models are built separately for OWCEB on account of the characteristics of OSWCS and OHWCS. Additionally, the cost saving models including the production cost saving, the operation cost saving and total cost saving are established. Then, the mathematical models are demonstrated with a numerical example intuitively. Furthermore, we analyze several parameters that influence the effectiveness of battery reduction due to the application of an opportunistic wireless-charging system on an electric bus. Finally, some points worth discussing in this work are performed.