Flow in an idealized bentonite polymer composite geosynthetic clay liner (BPC-GCL) containing bentonite comprising two idealized circular granules was simulated using a COMSOL hydrodynamic model. The effect of the polymer rheology properties, including viscosity, surface tension, and contact angle, on the hydraulic conductivity of BPC-GCLs was investigated. The results showed that the hydraulic conductivity of BPC-GCLs significantly decreased by 2–4 orders of magnitude with polymer loadings of 3.3%, 6.5%, and 9.8% compared to conventional geosynthetic clay liners (GCLs). The polymer rheology properties are critical to the residence time and the hydraulic conductivity of BPC-GCLs. The residence time increases with the viscosity, surface tension, and contact angle of polymer hydrogel. In the overall study, the hydraulic conductivities increased significantly from 2.80 × 10−9 m/s to 1.40 × 10−7 m/s when the residence time was insufficient. When the viscosity of the polymer hydrogel is 5000 Pa∙s, 1 × 104 Pa∙s, and 1 × 105 Pa∙s, the residence time of the polymer hydrogel in the domain of BPC-GCLs is 14 min, 23 min, and 169 min, respectively. When the surface tension of the polymer hydrogel is 0 N/m, 0.01 N/m, and 0.02 N/m, the residence time of the polymer hydrogel in the domain of BPC-GCLs is 9 min, 17 min, and 23 min, respectively. When the contact angle between the polymer hydrogel and the NaB granules is 30° to 60°, the residence time of the polymer hydrogel in the domain of BPC-GCLs is 9 min and 33 min. These few minutes can approximate the actual passage of several days in physical time. When the viscosity, the surface tension, and the contact angle are higher than 1 × 106 Pa∙s, 0.03 N/m, and 60°, the residence time of the polymer hydrogel in the domain of BPC-GCLs tends to be very long, which means that a very low hydraulic conductivity of BPC-GCLs can be maintained in the very long term. This research unveils a nuanced and profound correlation between the rheological properties of the polymer hydrogel and the resulting hydraulic conductivity. This discovery enhances the understanding of the potential to tailor hydrogel characteristics for BPC-GCLs. The advanced model developed in this study also lays the groundwork for constructing a more realistic model that considers irregular geometries, interconnected pores, and diverse polymer distributions within the pore spaces.