Vehicles crossing bridge structures respond dynamically to the bridge's vibrations. An acceleration signal collected within a moving vehicle contains a trace of the bridge's structural response, but also includes other sources such as the vehicle suspension system and surface roughness-induced vibrations. This paper introduces two methods for the bridge system identification using data collected by a network of moving vehicles. The contributions of the vehicle suspension system are removed by deconvolving the vehicle response in frequency domain. The first approach utilizes the vehicle transfer function, and the second uses EEMD method. Next, roughness-induced vibrations are extracted using second-order blind identification (SOBI) method. After these two processes the resulting signal is equivalent to the readings of mobile sensors that scan the bridge's dynamic response. Structural modal identification using mobile sensor data has been recently introduced as STRIDEX algorithm. The processed mobile sensor data is analyzed using STRIDEX to identify the modal properties of the bridge. The performance of the methods is validated on numerical case studies of a long single-span bridge monitored via a network of moving vehicles. The analyses consider three road surface roughness patterns. Results show that the proposed algorithms are successful in extracting pure bridge vibrations, and produce accurate and comprehensive modal properties of the bridge. The study shows that the proposed transfer function method can efficiently deconvolve the linear dynamics of a moving vehicle. EEMD method is able to extract vehicle dynamic response without a-priori information about the vehicle. This study is the first proposed methodology for complete bridge modal identification, including operational natural frequencies, mode shapes and damping ratios using \textit{moving vehicles sensor data}.