Bentonites from the 10th Khutor deposit (Republic of Khakassia, Russia) are considered a potential buffer material for isolation of radioactive waste in the crystalline rocks of Yeniseyskiy site (Krasnoyarskiy region). This study presents the results of a series of permeameter experiments with bentonite compacted to dry densities of 1.4, 1.6, and 1.8 g/cm3, saturated and permeated by the artificial groundwater from Yeniseyskiy Site. Permeation was conducted at hydraulic gradients of 180–80,000 m/m to simulate potential hydraulic conditions in the early post-closure phase of a deep geological repository (DGR). The respective swelling pressures of 0.8 ± 0.3, 2.2 ± 0.6, and 6.3 ± 0.3 MPa and permeabilities of (27 ± 15) × 10−20, (3.4 ± 0.8) × 10−20, and (0.96 ± 0.26) × 10−20 m2 were observed for the hydraulic gradient of 2000 m/m, which is recommended for the determination of undisturbed swelling pressures and permeabilities in permeameter experiments. Upon incremental increases in the hydraulic gradient, swelling pressures at all densities and permeability at the density of 1.8 g/cm3 remained unchanged, whereas permeabilities at 1.4 and 1.6 g/cm3 decreased overall by a factor of approximately 5 and 1.7, respectively. Seepage-induced consolidation and/or reorganisation of bentonite microstructure are considered possible reasons for these decreases.