Numerous offshore wind turbines (OWTs) with bucket foundations have been installed in seismic regions. Compared to the relative development of monopiles (widely installed), seismic design guidelines for bucket-supported OWTs still need to be developed. Moreover, scour around bucket foundations induced by water–current actions also creates more challenges for the seismic design of OWTs. In this study, a simplified seismic analysis method is proposed that incorporates the soil–structure interaction (SSI) for the preliminary design of scoured bucket-supported OWTs, aiming to balance accuracy and efficiency. The dynamic SSI effects are represented using lumped parameter models (LPMs), which are developed by fitting impedance functions of the soil–bucket foundation obtained from the four-spring Winkler model. The water–structure interaction is also considered by the added mass in seismic analysis. Based on the OpenSees 3.3.0 platform, an integral model is established and validated using the three-dimensional finite element method. The results indicate that the bucket-supported OWT demonstrates greater dynamic impedance and first-order natural frequency compared to the monopile-supported OWT, which has an increased seismic response. Seismic spectral characteristics and intensities also play an important role in the responses. Additionally, scour can change the bucket impedance functions and the frequency characteristics of the OWT system, leading to a significant alteration in the seismic response. Scour effects may be advantageous or disadvantageous, depending on the spectral characteristics of seismic excitations. These findings provide insights into the seismic response of bucket-supported OWTs under scoured conditions.