This paper presents an investigation about the stationary and transient analyses of suspension bridges subjected to spatially varying ground motions including the site response effect. The Bosphorus Suspension Bridge, which connects Europe to Asia in Istanbul, Turkey is selected as a numerical example. The spatial variability of ground motions between the support points is taken into consideration with the coherency function, which arises from three sources: incoherence, wave-passage and site-response effects. The Heaviside Modulating Function has been used throughout the study for computing the transient responses. At the end of the study, the results are compared with each other in two groups as homogeneous-heterogeneous and stationary-transient responses. It is observed that the response values obtained for the heterogeneous soil condition cause larger response values than those of the homogeneous soil condition. Also the greater the differences between the soil conditions, the greater the response values. It is also noticed that the stationary response values are larger than those of the transient responses. Based on the obtained results, the stationary assumption can be accepted as satisfactory for the considered ground motion duration.