Digital contact tracing is being used by many countries to help contain COVID-19's spread in a post-lockdown world. Among the various available techniques, decentralized contact tracing that uses Bluetooth received signal strength indication (RSSI) to detect proximity is considered less of a privacy risk than approaches that rely on collecting absolute locations via GPS, cellular-tower history, or QR-code scanning. As of October 2020, there have been millions of downloads of such Bluetooth-based contract-tracing apps, as more and more countries officially adopt them. However, the effectiveness of these apps in the real world remains unclear due to a lack of empirical research that includes realistic crowd sizes and densities. This study aims to fill that gap, by empirically investigating the effectiveness of Bluetooth-based contact tracing in crowd environments with a total of 80 participants, emulating classrooms, moving lines, and other types of real-world gatherings. The results confirm that Bluetooth RSSI is unreliable for detecting proximity, and that this inaccuracy worsens in environments that are especially crowded. In other words, this technique may be least useful when it is most in need, and that it is fragile when confronted by low-cost jamming. Moreover, technical problems such as high energy consumption and phone overheating caused by the contact-tracing app were found to negatively influence users' willingness to adopt it. On the bright side, however, Bluetooth RSSI may still be useful for detecting coarse-grained contact events, for example, proximity of up to 20m lasting for an hour. Based on our findings, we recommend that existing contact-tracing apps can be re-purposed to focus on coarse-grained proximity detection, and that future ones calibrate distance estimates and adjust broadcast frequencies based on auxiliary information.