Abstract: Bursty bulk flows (BBFs) were viewed as multi-scale carriers of energy, flux and momentum in the magnetosphere. Previous research found that, in addition to eddy interactions, wavy fluctuations might also serve as important constituents of the turbulence. However, there were lacking evidence of certain wave modes associated with BBFs, especially in the kinetic regime. Measurements of the ion kinetic scale density fluctuations have also not been reported in the BBFs. In this research, we investigated the density as well as magnetic field fluctuation in order to understand the compressible turbulence associated with the BBF in a different perspective. We have found the multi-scale anti correlation betweenn-B(1 - 60 s), exhibiting a similar features of the pressure-balanced structures (PBSs) in the solar wind. We report direct evidence of slow magnetosonic waves in the compressible turbulence by checking the plasma compressibility, Alfvén ratio, magnetic compressibility and dispersion relation. Furthermore, the fluctuations of density and magnetic field have similar double slope spectrum and kurtosis. We suggest that these slow-mode waves may serve as an important constituent of the turbulence in the plasma sheet.