When a rising bubble in a Newtonian liquid reaches the liquid-air interface, it can burst, leading to the formation of capillary waves and a jet on the surface. Here, we numerically study this phenomenon in a yield-stress fluid. We show how viscoplasticity controls the fate of these capillary waves and their interaction at the bottom of the cavity. Unlike Newtonian liquids, the free surface converges to a non-flat final equilibrium shape once the driving stresses inside the pool fall below the yield stress. Details of the dynamics, including flow energy budgets, are discussed. The work culminates in a regime map with four main regimes, all with different characteristic behaviours.