Locating the informative frequency band of rolling bearing fault signals is of great significance for feature extraction and fault diagnosis. Benefiting from the adjustable center frequency and bandwidth as well as the similarity to impulse-like characteristics induced by bearing failures, Morlet wavelets are commonly used in resonance demodulation. However, the fault impulses are completely masked by the noise at a very low signal-to-noise ratio (SNR), which imposes many limitations on the existing wavelet parameter selection strategies and frequency band optimization methods. In this paper, an adaptive Morlet wavelet-based iterative filtering (AMIF) method is proposed for frequency band optimization under low SNR. The resonance frequency band is pinpointed based on adaptive Morlet wavelet filter banks, with off-band noise being canceled and fault features being refined during the filtering process. Additional iterative operations are leveraged to enhance fault features of in-band signals to facilitate the optimization of the filtering parameters. The effectiveness of the proposed AMIF method and its superiority over the WPT-based Kurtogram are verified through simulation and experimental analysis. According to the results, AMIF can effectively isolate the impulsive fault features even from overwhelming background noise.