Dispersal patterns can dictate genetic population structure and, ultimately, population resilience, through maintaining gene flow and genetic diversity. However, geographical landforms, such as peninsulas, can impact dispersal patterns and thus be a barrier to gene flow. Here, we use 13 375 genome-wide single-nucleotide polymorphisms (SNPs) to evaluate genetic population structure and infer dispersal patterns of the Western Grasswren Amytornis textilis textilis (WGW, n = 140) in the Shark Bay region of Western Australia. We found high levels of genetic divergence between subpopulations on the mainland (Hamelin) and narrow peninsula (Peron). In addition, we found evidence of further genetic sub-structuring within the Hamelin subpopulation, with individuals collected from the western and eastern regions of a conservation reserve forming separate genetic clusters. Spatial autocorrelation analysis within each subpopulation revealed significant local-scale genetic structure up to 35 km at Hamelin and 20 km at Peron. In addition, there was evidence of male philopatry in both subpopulations. Our results suggest a narrow strip of land may be acting as a geographical barrier in the WGW, limiting dispersal between a peninsula and mainland subpopulation. In addition, heterogeneous habitat within Hamelin may be restricting dispersal at the local scale. Furthermore, there is evidence to suggest that the limited gene flow is asymmetrical, with directional dispersal occurring from the bounded peninsula subpopulation to the mainland. This study highlights the genetic structure existing within and between some of the few remaining WGW subpopulations, and shows a need to place equal importance on conservation efforts to maintain them in the future.