The presence of microbubble significantly influences the rheological properties of a jet, thereby considerably increasing the complexity of the jet instability problem. However, the instability of microbubble jets has been rarely studied, and their breakup mechanism remains obscure. The present study was focused on conducting a comprehensive analysis of bubble jet flows. A high-precision experimental system was constructed to extract the time-series signals of each cross-sectional profile along the axial direction of a jet. Glycerol solutions with three different bubble volume fractions were prepared, and the standard deviation, spectral relationship, and nonlinear dynamical behavior (i.e., autocorrelation, phase space trajectory, Poincaré section, and Lyapunov exponent) were studied. The detailed development process of small surface disturbances in space was assessed, and the influence of variations in the bubble volume fraction on the nonlinear dynamics of the jet was examined. The results demonstrate that microbubbles can significantly change the energy transfer relationship between various sections of a jet and enhance the periodicity of the signal.