Slightly SBS-modified bitumen binders have been applied for the asphalt concrete impermeable layer of pumped storage power stations (PSPSs) in China. However, the storage stability and aging resistance of slightly SBS-modified bitumen are big concerns. In this study, three different types of slightly SBS-modified bitumen binders were evaluated by using a commonly used virgin bitumen and a normal SBS polymer-modified bitumen as references. All of the bitumen binders were subjected to short-term and long-term aging that were simulated by using a 5 h and 24 h thin film oven test (TFOT), respectively. A Fourier transform infrared (FTIR) spectroscopy test, storage stability test, dynamic shear rheological test, stress relaxation test, and direct tensile (DT) test were carried out to obtain insight into the storage stability and aging resistance. FTIR analysis indicated that slightly SBS modified bitumen exhibited serious aging of base bitumen together with higher polymer degradation. The aging indexes obtained from the carbonyl index and the polybutadiene (PB) index can well rank the aging resistance. Slightly SBS-modified bitumen binders had excellent storage stability, and even after a long-term period of 7 days of storage, the complex modulus and phase angle remained fairly constant. The rheological master curves were constructed to investigate the effects of short-term and long-term aging. Slightly modified bitumen binders were well identified by the plateau of the phase angle master curves. The aging resistance was well distinguished by the deviation of the complex modulus master curve using unaged bitumen as a baseline. It was found that three types of slightly SBS-modified bitumen binders exhibited inconsistent aging resistance in terms of rheological aging index. The relative change of the initial instantaneous modulus and the modulus relaxation rate was able to explain the relaxation properties. With respect to the direct tensile test, the increase in stiffness modulus and the loss of ultimate tensile strain can be used to evaluate the susceptibility of bitumen aging. An attempt was made to establish the relationship of the aging index between FTIR analysis, rheological properties, and low-temperature performance. It was found that the relationship among these aging indexes was weak. In general, slightly SBS modified bitumen should be well designed to obtain good aging resistance and low-temperature performance. Highly modified bitumen is foreseen to be promising in the case of extremely low temperatures and long-term durability.