Currently, buses are equipped with anti-rollover systems to prevent vehicle rollovers that cause numerous traffic deaths each year. In order to improve the functioning of the existing anti-rollover systems, this study proposes a new method to predict the lateral transfer ratio (LTR) of a bus to achieve early detection of bus rollover risks. This early rollover detection method is a combination of the LTR, the grey model, and a buffer operator, which can predict the LTR trend, for providing a certain timing advance to the anti-rollover control system. First, an estimation equation is proposed to better estimate the LTR, and validated using Simulink and TruckSim. Then, a basic grey model is utilized with the estimated LTR to predict the future LTR. However, it is found that though the grey model-based LTR (G-LTR) can provide significant timing advances, the LTR prediction curves obtained from the complex handling stability tests contain sharp wave crests that may cause an unintended initiation of the anti-rollover systems. Therefore, to overcome this drawback and make this method practical, a buffer operator is added to form a new rollover index (buffer grey LTR or BG-LTR) that can completely predict the future trend of the LTR based on the current and previous values. Eventually, the peak LTR value is reduced from 2.758 to 0.743 for the case of a 90-km/h double lane change (DLC). Additionally, the predicted timing advance with a minimum of approximately 0.19 s is sufficient for all the different handling tests. Overall, the BG-LTR can extend the application of the anti-rollover systems to a wider speed range and is appropriate for all the complex handling of stability trials.