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 BLE a potential inter-vehicle communication technology, either replacing or complementing other vehicle-to-vehicle (V2V) technologies (such as the yet to be deployed DSRC). 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: (1) undirected advertisements and scanning (unconnected mode) and (2) using the central and peripheral modes of the Generic Attribute Profile (GATT) connection (connected mode). This paper investigates quantitative and qualitative advantages and disadvantages of both approaches and proposes a communication framework based on the central/peripheral mode, which uses a random role 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. The paper further discusses other limitations, prospects, and potential applications of a BLE-based communication framework for VANETs.