The primary objective of this study is to model and predict the rheological properties of SBS-modified bitumen under the influence of polymer content (0–6%), loading frequency (0.1–40 rad/s), and service temperatures (52–76 °C) using statistical regression models and artificial neural networks (ANNs). To this end, the rheological behavior and rutting resistance of bitumen containing 3, 4, 5, and 6% SBS were evaluated through temperature sweep and frequency sweep tests. Subsequently, the rheological properties of the bitumen were predicted as a function of polymer content, loading intensity, and service temperature using regression and ANN models. The results indicate that increasing the loading frequency and SBS content significantly enhances the rheological parameters of the bitumen. Analysis of the G*/Sinδ index shows that adding SBS improves rutting resistance across different frequency ranges, with a direct relationship observed with increasing SBS content and an inverse relationship with increasing loading frequency. Moreover, reducing the frequency and increasing the applied stress considerably decreases the rutting resistance, with this performance reduction being much more pronounced in unmodified bitumen compared to polymer-modified bitumen. Finally, the results demonstrate that the proposed models accurately predict the rheological behavior of bitumen and can be effectively employed during the design phase, prior to pavement construction, to optimize design, reduce performance uncertainties, and substantially save laboratory time and costs.