We investigate the dynamics of the buoyancy-driven rise of a bubble inside a viscoplastic material when it is subjected to an acoustic pressure field. To this end, we develop a simplified model based on the Lagrangian formalism assuming a pulsating bubble with a spherical shape. Moreover, to account for the effects of a deformable bubble, we also perform detailed two-dimensional axisymmetric simulations. Qualitative agreement is found between the simplified approach and the detailed numerical simulations. Our results reveal that the acoustic excitation enhances the mobility of the bubble, by increasing the size of the yielded region that surrounds the bubble, thereby decreasing the effective viscosity of the liquid and accelerating the motion of the bubble. This effect is significantly more pronounced at the resonance frequency, and it is shown that bubble motion takes place even for Bingham numbers (Bn) that can be orders of magnitude higher than the critical Bn for bubble entrapment in the case of a static pressure field.