Demodulation analysis is one of the most effective methods for bearing fault diagnosis. However, in practical applications, the interferences from ambient noises or other rotating components may create great challenges to demodulation analysis and thus decrease its effectiveness. Generally, a selection procedure for the most informative frequency band (IFB) is usually implemented in advance to extract the fault features that are hidden by the interferences. The fast kurtogram (FK) has been utilized as a benchmark for the IFB selection. Although designed to identify the most impulsive part of the signal, the FK is inevitably affected by the fault-irrelevant impulsive and cyclostationary interferences due to the dual sensitiveness to the impulsiveness and cyclostationarity of the kurtosis, and thus it may produce a misleading band for demodulation. To address this issue, a novel and robust IFB selection method based on the fault energy of correntropy (named FECgram) is proposed in this paper to replace the FK, through which the IFB can capture the fault symptom without being influenced by the fault-irrelevant impulsive and cyclostationary interferences. The superiority of the FECgram in combination with the squared envelope spectrum (SES) is validated on both simulation data and three different challenging experimental datasets.