We examine the effectiveness of the OWNS-R model in analysing the stability of convective disturbances in boundary-layer flows exhibiting laminar separation bubbles (LSBs). The LSBs are generated through the introduction of surface indentations over a nominally flat surface. Results highlight the effectiveness of the one-way stabilised marching procedure in scenarios without or with small LSB regions. However, they also reveal the limitations of current OWNS methodologies when applied to surface indentations that feature relatively larger LSBs. To address this shortcoming, we propose a novel modal one-way approach, M-OWNS, which enables numerically stable marching through relatively larger LSB regions.