While public transportation (PT) plays a critical role in urban mobility, the discomfort and the disutility of the last-mile trips make PT unattractive. We study the feasibility of shared autonomous vehicles (AV) as an on-demand alternative to fixed-route buses for last-mile travel. To this end, the bus routes that operate along the edges of the PT network in Bursa, Turkey are selected. The origin and destination (OD) pairs of the trips made on these bus routes are inferred at an individual level. The vehicle routing problem is then formulated by considering the proposed transportation service. Several solution methods are developed for both solution construction and solution improvement phases of the problem. To assess solution methods with real-world data, an agent-based simulation framework is built. It is found that the solution methods successfully solved a dynamic problem. The results show that the integration of PT using AVs is well-suited to improve the service quality and energy efficiency in the last-mile mobility.