Wheelset-bearing weaker fault feature extraction from multi-impulsive signals under time-varying speed conditions still presents challenges because of unrelated high amplitude cyclic component interferences and rotational speed fluctuations. To address these issues, a more robust impulsiveness index for assessing fault-related information and a more accurate optimal resonance band (ORB) localization method for weaker fault feature extraction are proposed in the angle domain. On these bases, a fault diagnosis framework for the wheelset bearings under time-varying speed conditions, named bidirectional iterative search and order spectrum segmentation based on RCCOD (BISOSSRCCOD), is developed. The proposed method is composed of four steps: 1) obtain the angle domain signals with the aid of speed signals of the wheelset; 2) determine the initial range of the ORB; 3) obtain the accurate range of ORB and center order (CO); and 4) perform envelope analysis of the selected segment for fault detection in the angle domain. The effectiveness of the proposed method is validated using both simulated signals and experimental data. The results reveal that the proposed indicator can resist various interferences and is more suitable for weaker fault feature extraction from multi-impulsive signals. The proposed BISOSSRCCOD method is superior to the ORB location for bearing failure identification under time-varying speed conditions.