In this paper, the geometry of a supersonic inlet isolator is modified by the introduction of a two-dimensional (2D) bump to control the complex lip shock wave/boundary layer interaction (SWBLI). The bump is of general shape whose profile is designed primarily based on the inviscid theory of oblique shock waves, which accommodates the effect of freestream conditions; particularly, the flow Mach number. Further, the geometric constraints of the inlet are taken into consideration to generate a contoured bump. This well-designed generic bump is tested in the range of flight Mach number of 2.5 to 3.8 through numerical computations. The adopted computational methods are validated with the available experimental data. Results showed that the modified inlet using the present generic bump changes the internal shock structure, weakens the intensity of SWBLI, and subsequently reduces shock reflection phenomena which are prevalent in baseline inlet. The wall characteristics such as separation bubble (SB), skin friction, and total pressure loss are found to be reduced in inlet with bump. The SB in baseline inlet typically corresponds with the geometric profile of the bump. As a result, ramp of baseline inlet is apparently replaced by this generic bump, which eliminates the low momentum fluid adjacent to the wall and the passage of modified inlet is found to be mostly occupied by high momentum supersonic flow. The flow control and associated performance improvement are linked with this modification of supersonic inlet isolator.