The results of theoretical studies of the resonant quenching and ion-pair formation processes induced by collisions of Rydberg atoms with highly polar molecules possessing small electron affinities are reported. We elaborate an approach for describing collisional dynamics of both processes and demonstrate the predominant role of resonant quenching channel of reaction for the destruction of Rydberg states by electron-attaching molecules. The approach is based on the solution of the coupled differential equations for the transition amplitudes between the ionic and Rydberg covalent terms of a quasimolecule formed during a collision of particles. It takes into account the possibility of the dipole-bound anion decay in the Coulomb field of the positive ionic core and generalizes previous models of charge-transfer processes involving Rydberg atoms to the cases, when the multistate Landau-Zener approaches become inapplicable. Our calculations for ( ) nl Rb atom perturbed by C H SO 2 4 3 , CH CHCN 2 , CH NO 3 2 , CH CN 3 , C H O 3 2 3 , and C H O 3 4 3molecules show that the curves representing the dependence of the resonant quenching cross sections on the principal quantum number n are bell-shaped with the positions of maxima being shifted towards lower values of n and the peak values, ( ) s max q , several times higher than those for the ion-pair formation, ( ) s max i . We obtain a simple power relation between the energy of electron affinity of a molecule and the position of maximum in n-dependence of the resonant quenching cross section. It can be used as an additional means for determining small binding energies of dipole-bound anions from the experimental data on resonant quenching of Rydberg states by highly polar molecules.