Historically, monitoring possible deformations in suspension bridges has been a crucial issue for structural engineers. Therefore, to understand and calibrate models of the “load-structure-response”, it is essential to implement suspension bridge monitoring programs. In this work, due to increasing GNSS technology development, we study the movement of a long-span bridge structure using differenced carrier phases in adjacent epochs. Many measurement errors can be decreased by a single difference between consecutive epochs, especially from receivers operating at 10 Hz. Another advantage is not requiring two receivers to observe simultaneously. In assessing the results obtained, to avoid unexpected large errors, the outlier and cycle-slip exclusion are indispensable. The final goal of this paper is to obtain the relative positioning and associated standard deviations of a stand-alone geodetic receiver. Short-term movements generated by traffic, tidal current, wind, or earthquakes must be recoverable deformations, as evidenced by the vertical displacement graphs obtained through this approach. For comparison studies, three geodetic receivers were positioned on the Assut de l’Or Bridge in València, Spain. The associated standard deviation for the north, east, and vertical positioning values was approximately 0.01 m.