Connected vehicle technologies present new opportunities to minimize energy consumption in vehicles. Much of the prior work has focused on the impact of vehicle-to infrastructure (V2I) communication on energy savings. Here, we analyse the impact of connectivity on both energy savings and battery degradation reduction for an electric bus. Dynamic programming is employed to optimize the velocity profile of a single electric bus passing through a traffic intersection under a V2I regime wherein the intersection timing of the traffic light is known a priori. The optimization seeks to minimize the overall cost function consisting of the electric energy consumption and battery degradation. Simulations have been conducted for both the connected vehicle case and the baseline case without connectivity. Three different battery sizes were investigated, and the results indicate that connectivity confers the greatest cost savings for the smallest battery. An overall cost savings of 27% can be realized by using connectivity to reduce both energy consumption and battery degradation.