The component of rolling bearing vibration is difficult to be determined and the instantaneous rotational frequency is hard to be estimated accurately under varying conditions without a tachometer. Most studies mainly rely on the prior speed knowledge and focus on the spectrum distortion caused by time-varying impacts, while little attention has been paid to tacholess bearing fault feature extraction under varying conditions. A novel tacholess quantitative characterization method is proposed for rolling bearing fault feature extraction under varying conditions. The vibration Hilbert envelope is utilized to extract the bearing fault feature. To quantitatively describe the relationship among vibration envelope components, a model based on source hypothesis for feature extraction as well as a quantitative characterization method is proposed. The instantaneous frequencies of spectrogram ridges are estimated consecutively based on the maximum energy-minimum curvature criterion by resorting to the time-frequency reassignment and reconstruction capability of the synchrosqueezed wavelet transform. To reduce the influence of various interference in the generalized demodulated vibration envelope on the quantitative results, a method of interference suppression and stationarization reset under varying conditions is proposed based on the selective reconstruction and the generalized demodulation. The proposed method is applied to analyze the simulated signal and bearing vibration data. It takes about 3 s to extract the features of envelope component with length of 10 k points under different source hypotheses. Meanwhile, the fault characteristics of inner race fault bearing with a speed change of about 300 r/ min in 2 s and that of the compound fault bearing with a speed change of about 200 r/ min in 2 s are quantitatively characterized without a tachometer.