Crowdsourcing is a powerful technique for bootstrapping sensing systems that are based on wireless signals. For example, wireless sensing systems can ask users to contribute training data and localization systems (such as WiFi fingerprinting) can take advantage of wireless measurements provided by users of the system. Indeed, previous research has demonstrated that crowdsourcing can reduce labor efforts needed to deploy and initialize wireless sensing systems by several orders of magnitude, without compromising on system performance. Despite the many benefits of crowdsourcing, current methods suffer from one significant drawback, namely that they are highly sensitive to variations in devices capturing the measurements. Indeed, as we demonstrate in this paper, cross-device variations can decrease performance of crowdsourced bootstrapping approaches up to 70of radio maps used for localization and to make them robust against cross-device variations in wireless signals. We evaluate our framework by considering WiFi fingerprinting based localization as a representative example of applications that benefit from our approach. Our results demonstrate up to 1.8m localization error, and 18.7.