This work utilizes an immersed boundary (IB) method to simulate the effects of arrays of discrete bleed ports in controlling shock wave/turbulent boundary layer interactions. Both Reynolds averaged Navier-Stokes (RANS) and hybrid large-eddy/Reynolds-averaged Navier-Stokes (LES/RANS) turbulence closures are used with the IB technique. The approach is validated by conducting simulations of Mach 2.5 flow over a perforated plate containing 18 individual bleed holes. Predictions of discharge coefficient as a function of bleed plenum pressure are compared with experimental data. Simulations of an impinging oblique shock/boundary layer interaction at Mach 2.45 with and without active bleed control are also performed. The 68-hole bleed plate is rendered as an immersed object in the computational domain. Wall pressure predictions show that, in general, the LES/RANS technique under-estimates the upstream extent of axial separation that occurs in the absence of bleed. Good agreement with Pitot-pressure surveys throughout the interaction region is obtained, however. Active suction completely removes the separation region and induces local disturbances in the wall pressure distributions that are associated with the expansion of the boundary layer fluid into the bleed port and its subsequent re-compression. Predicted Pitot-pressure distributions are in good agreement with experiment for the case with bleed. Swirl strength probability-density distributions are used to estimate the evolution of turbulence length-scales throughout the interaction, and the effects of bleed on the amplification of Reynolds stresses are highlighted. Finally, simple improvements to engineering-level bleed models are proposed based on the computational results.