Vehicular visible light communication (VVLC) has emerged as a promising field of research, garnering considerable attention from scientists and researchers. VVLC offers a potential solution to enable connectivity and communication between travelling vehicles along the road by using their existing headlights (HLs) and taillights (TLs) as wireless transmitters and integrating photodetectors (PDs) within the car front or car-back as wireless receivers. However, VVLC encounters more challenges than indoor VLC, particularly in vehicle-to-vehicle (V2V) communication, where vehicle mobility disrupts the establishment of direct communication links. To address this, we propose a multi-hop relay system wherein intermediate vehicles act as wireless relays to maintain a line-of-sight (LoS) link. In this paper, we investigate the performance of a bidirectional multi-hop relay V2V-VLC system that operates in both the forward and backward directions. Based on realistic ray tracing channel models, we derive a closed-form expression for the full bidirectional communication range. We also analyze how the transceiver's parameters and the number of relays affect the system performance. Our results show that the proposed bidirectional multi-hop relay system can extend the direct transmission range by more than 19 m with only a hop relay.