In this work, the dynamics of bubbly flow in a dielectric ferrofluid under a uniform magnetic field has been numerically studied by a self-correcting procedure-based lattice Boltzmann flux solver. The investigation cases focus specifically on two bubbles merging and a single bubble rising in ferrofluid with a large density ratio under an applied uniform magnetic field. By accounting for the effects of the magnetic field intensity, susceptibility, Reynolds number, and Eotvos number, the mechanisms of bubble motion and deformation in the ferrofluid under the external magnetic field are analyzed.