Studies of the e+e- annihilation into open-bottom final states are very important for understanding of the properties and nature of the bottomonium and bottomonium-like states. We report the first measurement of the inclusive σ(e+e− → bb̄ → DsX) and σ(e+ e− → bb̄ → D0X) cross sections in the energy range from 10.63 to 11.02 GeV. Based on these results, we determine σ(e+ e− → Bs X) in the same energy range. The achieved accuracy in σ(e+ e− → Bs X) is much higher than in the method with a full reconstruction of one Bs meson. The results are obtained using the data collected with the Belle detector at the KEKB asymmetric-energy e+ e− collider.