A novel optical soliton dynamics phenomenon, called "invisible" pulsation, has gradually attracted extensive interest in recent years, which can only be identified effectively with the help of real-time spectroscopy technique, i.e., dispersive Fourier transformation (DFT). In this paper, based on a new bidirectional passively mode-locked fiber laser (MLFL), the "invisible" pulsation dynamics of soliton molecules (SMs) is systematically studied. It is indicated that the spectral center intensity, pulse peak power and relative phase of SMs are periodically changed during the "invisible" pulsation, while the temporal separation inside the SMs is constant. The degree of spectral distortion is positively correlated with the pulse peak power, which verifies that self-phase modulation (SPM) is the inducement of spectral distortion. Finally, the universality of the SMs "invisible" pulsation is further experimentally verified. We believe our work is not only conducive to the development of compact and reliable bidirectional ultrafast light sources, but also of great significance to enrich the study of nonlinear dynamics.