Indoor Positioning Systems (IPSs) hold significant potential for enhancing visitor experiences in cultural heritage institutions. By enabling personalized navigation, efficient artifact organization, and better interaction with exhibits, IPSs can transform the modalities of how individuals engage with museums, galleries and libraries. However, these institutions face several challenges in implementing IPSs, including environmental constraints, technical limits, and limited experimentation. In other contexts, Received Signal Strength (RSS)-based approaches using Bluetooth Low Energy (BLE) and WiFi have emerged as preferred solutions due to their non-invasive nature and minimal infrastructure requirements. Nevertheless, the lack of publicly available RSS datasets that specifically reflect museum environments presents a substantial barrier to developing and evaluating positioning algorithms designed for the intricate spatial characteristics typical of cultural heritage sites. To address this limitation, we present BAR, a novel RSS dataset collected in front of 90 artworks across 13 museum rooms using two different platforms, i.e., Android and iOS. Additionally, we provide an advanced position classification baseline taking advantage of a proximity-based method and $k$-NN algorithms. In our analysis, we discuss the results and offer suggestions for potential research directions.