In recent years, we have witnessed a growing interest in Vehicular Networks from both the research community and industry. Several potential applications of Vehicular Networks are envisioned such as road safety and security, streaming services, traffic monitoring and driving comfort, just to mention a few. It is critical that the existence of convenience or driving comfort services do not negatively affect the performance of safety services. In essence, the dissemination of safety services or the discovery of convenience applications require the communication among service providers and service requesters through constrained bandwidth resources. Therefore, service discovery techniques for vehicular networks must efficiently use the available common resources. In this paper, we present a bandwidth-efficient and scalable hybrid adaptive service discovery protocol (VSDP) for Vehicular Networks. VSDP aims at providing high success ratio while guaranteeing low response time and good scalability when the number of requests increases. Our proposed protocol finds the service provider and its routing information simultaneously which results in overall bandwidth savings. It uses diverse channels to exchange discovery and routing packets, thereby decreasing the congestion on single channels and decreasing the delay of service discovery. Our proposed service discovery protocol adapts the advertisement zone size of service providers based on an efficient adaptation mechanism that takes into consideration network condition and application requirements. The adaptation process is based on an adjustment technique and a prediction technique. We discuss the implementation of our protocol, present its proof of correctness as well as the performance evaluation through an extensive set of simulation experiments and using different mobility models. Our results show the scalability of our protocol. They indicate that our techniques can achieve significant success rate (more than 90 percent), while guaranteeing low response time (in the order of milliseconds) and low bandwidth usage when compared to existing service discovery techniques.