The prevalence of ride-sharing services presents a fundamental trade-off between the operational costs and the users' convenience. While ride-sharing operations reduce operational costs, users may experience certain inconveniences, such as longer ride times when sharing their rides with others. Along with the development of ride-sharing services, the emergence of new techniques, such as electric vehicles and autonomous techniques, has drawn academic interests in operations research to apply a more eco-friendly and comfortable mode of transport. The Electric Autonomous Dial-A-Ride Problem (the E-ADARP) was first introduced by \cite{bongiovanni2019electric}, which consists in designing a set of minimum-cost routes for a fleet of electric autonomous vehicles (EAVs) by scheduling them to provide ride-sharing services for users specifying their origins and destinations. In this work, we emphasize the conflicting interests of service providers and users in the objective function of the E-ADARP and investigate the Bi-objective E-ADARP (hereafter BO-EADARP). The two objectives of the BO-EADARP are the total travel time of all vehicles and the total excess user ride time of all users. We propose an exact algorithm to solve the problem. In the numerical study, we solve the BO-EADARP instances and the classical BO-DARP instances with our proposed method and methods in the literature (e.g., $\epsilon$-constraint methods). Our proposed method has demonstrated efficiency in terms of solution quality and computational time. We also analyze the hybridization among different methods, which help to enhance the performance.