In the present work, we generalize our previous work (Heydarzade and Darabi in arXiv:1710.04485, 2018 on the surrounded Vaidya solution by cosmological fields to the case of Bonnor-Vaidya charged solution. In this regard, we construct a solution for the classical description of the evaporating-accreting charged Bonnor-Vaidya black holes in the generic dynamical backgrounds. We address some interesting features of these solutions and classify them according to their behaviors under imposing the positive energy condition. Also, we analyze the timelike geodesics associated with the obtained solutions and show that some new correction terms arise in comparison to the case of standard Schwarzschild black hole. Then, we explore all these features for each of the cosmological backgrounds of dust, radiation, quintessence and cosmological constant-like fields in more detail.