We derive the bounce-averaged quasilinear (QL) operator in axisymmetric toroidal geometry using the standard QL formalism. When specialized to resonant ion cyclotron harmonic interactions, this operator predicts the same radiofrequency-induced radial diffusion as the orbit-averaged operator (Eriksson and Helander 1994 Phys. Plasmas1 308) obtained using action-angle variables. By assuming the wave field known as a superposition of toroidal and poloidal Fourier modes, the QL diffusion coefficients are written in a form which can be directly evaluated using the output of a spectral full-wave solver of Maxwell equations in toroidal plasmas.