Bluetooth Low Energy (BLE) is an energy-efficient radio communication technology that is rapidly gaining popularity for various Internet of Things (IoT) applications. While BLE was not designed specifically with vehicular communications in mind, its simple and quick connection establishment mechanisms make it a potential inter-vehicle communication technology, either replacing or complementing other V2V technologies (such as the yet to be deployed DSRC). Recently, there have been several efforts analyzing BLE performance in inter-vehicular communications, but these studies are still far from being comprehensive or conclusive. It is thus necessary to develop a new, accurate framework for BLE-based V2V communication. In particular, the wide range of parameter settings indicate great potential for BLE-based V2V communications. In this paper we propose a framework for V2V communication using BLE and evaluate its performance under various configurations. BLE uses two major methods for data transmission: undirected advertisements and scanning (unconnected mode) or using central and peripheral modes of the GATT connection (connected mode). This paper investigates quantitative and qualitative advantages and disadvantages of both approaches and proposes a communication framework based on the peripheral/central modes, which uses a random mode switching technique to ensure frequent communication opportunities between devices. Further, experiments on BLE-equipped Android devices are used to study the impacts of different framework parameters on communication performance, loss rates, and scalability. Based on the results, we explore the feasibility of applying the framework under various scenarios of V2V communications, especially for cases when infrastructure networks (Wi-Fi or Cellular) are unavailable. The paper further discusses prospects and potential applications of a hybrid framework of BLE communication and infrastructure networks for VANETs.