The most commonly adopted modifiers for bitumen are plastomeric thermoplastic copolymers, elastomeric thermoplastic copolymers, and crumb rubber. The performance of the modified binder, both short-term and long-term, depends on the interaction of the modifier with the base bitumen. This however is a function of the type of base bitumen, the modifier architecture, and its dosage, among many other factors. Typically a Multiple Stress Creep and Recovery test is used for characterizing the high-temperature performance of modified binders. The potential of MSCR test to capture the variation in rutting response with base binder type is not much investigated. The apparent viscosity of the material measured from a steady shear test is another protocol to characterize the material response related to rutting. In this study, a VG 30 base bitumen produced by two different processes, namely, air rectification and component blending are modified with an elastomeric polymer at different dosages. The modified binder is then characterized using the MSCR test and steady shear test, at RTFO-aged condition. It was found that as the polymer dosage is increased the sensitivity of polymer dosage to creep compliance and percent recovery depends on the shear stress level; at higher shear stress levels, the elastic response is more predominant. Considering the three stages in the flow curve, different stages were observed depending on the base binder type, polymer dosage, and test temperature. The study highlighted the need for considering the base binder type in the selection of polymer dosage along with other factors at the expected loading and temperature levels. Further investigations are needed to understand the underlying mechanism of reaction when base binders with different production processes are modified with polymers.