In this study, a comprehensive investigation of the stochastic analysis of a suspension bridge subjected to spatially varying ground motions is carried out for variable local soil cases and wave velocities. Bosphorus Suspension Bridge built in Turkey and connects Europe to Asia in Istanbul is selected as a numerical example. The spatial variability of the ground motion is considered with the incoherence, wave-passage and site-response effects. The incoherence effect is examined by taking into account Harichandran and Vanmarcke model, the site-response effect is outlined by using firm, medium and soft soil types, and the wave-passage effect is investigated by using 1000-2000, 500-1000, and 300-500 m/s wave velocities for the firm, medium and soft soils, respectively. Mean of maximum response values obtained from the spatially varying ground motions are compared with those of the specialized cases of the ground motion model. At the end of the study, it is seen that total displacements are dominated by dynamic component. The response values obtained for SMFF soil condition are generally the largest. When the varying local soil condition is considered, the variation of relative contributions of response components to the total response values for varying wave velocity cases is insignificant. Also, the variation of the wave velocity has important effect on the deck and towers total response values as compared with those of the constantly travelling wave velocity case. It is concluded that the site-response effect of ground motion on the response of suspension bridges is more important than that of the wave-passage, and the variation of the wave velocities depending on the local soil conditions, has important effects on the dynamic behavior of suspension bridge.