The adequate filling and quenching of small corner features are major challenges in the hot gas forming-quenching integrated process to manufacture complex-shaped boron steel tubular parts. As the filling and quenching of small corners occurs at the later stages of pressurized bulging, the temperature of the non-contact zone on the tube may rapidly reduce below the required forming temperature. Considering the tube forming process involves closed and invisible features, a single-sided die quenching experiment for B1800HS boron steel sheets was designed to simulate the in-die quenching process of steel tubes. Moreover, the cooling rate and hardness distribution of the die-contact and non-contact zones were analyzed. Specific bulging experiments for variable diameter tubular parts with axial corner were performed. The effects of bulging temperature and pressurizing rate on corner filling, microstructure, and mechanical properties were studied. The results confirmed that for a given thickness of B1800HS sheet, regions of rapid cooling rate and martensite transformation occurred under a smaller diameter of the non-contact circular zone. For the sheet with a thickness of 1.4 mm, when the diameter of the non-contact circular zone was reduced to lower than 20 mm, the complete martensitic transformation of the entire sheet could be realized. For the boron steel tubes, the filling of the axial corner was significantly improved with the increase of the initial bulging temperature and the gas pressurizing rate. At the initial bulging temperature of 900 °C, when the pressurizing rate increased from 1 MPa/s to 3 MPa/s, the obtainable minimum corner radius decreased from 24 mm to 16 mm. The width of the non-contact zone was less than the diameter (15 mm) that can achieve complete martensitic transformation in the single-sided die quenching experiment; therefore, a sufficiently high cooling rate can be obtained. However, when the pressurizing rate increased from 3 MPa/s to 5 MPa/s, the obtainable minimum corner radius only decreased from 16 mm to 12 mm. The limited filling of the corner was the result of a significant temperature drop during hot gas forming. Decreasing the cooling rates of the tube or increasing the pressurizing rates during the hot forming stage can extend the range of reasonable process parameters in the hot gas forming-quenching integrated process of the boron steel tubes.