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Recent experiments have shown that bending vibrations in laser-ionized SO₂ molecules can be directly mapped by time-resolved Coulomb explosion imaging (CEI). Here, we theoretically model the outcome of such IR pump – IR probe CEI experiment on SO₂ in full dimensionality.  We describe the pump step by solving the coupled-channel Schrödinger equation for the nuclear motion on two coupled Born-Oppenheimer potential-energy surfaces, SO₂ [X¹A₁ ] and SO₂⁺ [X²A₁ ]  (neutral and ionic electronic ground states, respectively). Employing ab initio calculated potential-energy surfaces, we calculate the  ionization yield as a function of time delay and OSO bond angle. We classically model the subsequent Coulomb explosion of  into the triply-charged S⁺+O⁺+O⁺ state and simulate the distribution of the asymptotic angles between the momentum vectors of O⁺ fragments as a function of the pump – probe time delay. In good agreement with our experimental data, this distribution clearly reveals a ~85 fs oscillation corresponding to bending vibrations in the SO₂⁺ [X²A₁ ] state.