To bring VANET into reality, it is crucial to devise routing protocols that can exploit the inherited characteristics of VANET environment to enhance the performance of the running applications. Previous studies have shown that a certain routing protocol behaves differently under different presumed mobility patterns. Bypass-AODV is a new optimization of the AODV routing protocol for mobile ad-hoc networks. It is proposed as a local recovery mechanism to enhance the performance of the AODV routing protocol. It shows outstanding performance under the Random Waypoint mobility model compared with AODV. However, Random Waypoint is a simple model that may be applicable to some scenarios but it is not sufficient to capture some important mobility characteristics of scenarios where VANETs are deployed. In this paper, we will investigate the performance of Bypass-AODV under a wide range of mobility models including other random mobility models, group mobility models, and vehicular mobility models. Simulation results show an interesting feature that is the insensitivity of Bypass-AODV to the selected random mobility model, and it has a clear performance improvement compared to AODV. For group mobility model, both protocols show a comparable performance, but for vehicular mobility models, Bypass-AODV suffers from performance degradation in high-speed conditions.