Bitumen, as a viscoelastic material, exhibits mechanical behavior that depends on temperature and loading rate; therefore, accurate characterization of its rheological properties is essential for predicting asphalt pavement distresses such as rutting. In this study, the effects of adding nanosilica and styrene–ethylene/propylene–styrene (SEPS) polymer on the performance of 85/100 penetration grade bitumen were investigated. To analyze the viscoelastic behavior, master curves of the complex shear modulus were constructed and compared using both the time–temperature superposition principle and the method based on temperature sweep data. To evaluate rutting resistance, two indicators—Superpave rutting parameter (G*/sinδ) and zero-shear viscosity (ZSV)—were employed. The results showed that nanosilica alone does not significantly improve rutting resistance, whereas the addition of SEPS, either individually or in combination with nanosilica, increases stiffness, enhances viscoelastic behavior, and improves the bitumen’s resistance to permanent deformation at high temperatures. Furthermore, comparison of the master curves demonstrated that the method based on temperature sweep data exhibits good agreement with the classical approach and can be considered a reliable alternative when frequency sweep testing is limited.