We calculate absorbtion cross-sections of B c mesons by π and ρ mesons with and without form factor including anomalous processes using meson exchange model. For calculating absorption cross sections of J/ψ − π, J/ψ − ρ and J/ψ − kaon, this approach has been used. After the suggestion for charmonium and bottomonium, it has been also suggested for heavy mixed flavor mesons that their production rate would be affected in the presence of quark gluon plasma. The enhancement of Bc production is expected due to QGP formation in heavy-ion experiments. However, in heavy-ion collisions it is also expected that the production rate of Bc meson can be affected due to the interaction with comovers. For the case of J/ψ absorption this problem has been studied quite extensively. The examination of Bc + hadron cross-section is important for extending this study to Bc. To have unambiguous interpretation of the the observed signal, the information of dissociation cross section is also important. In this work the absorption cross section of Bc meson are calculated with and without form factor, related cut-off parameters and using suitable choice of coupling constants. The total absorption cross section of Bc meson with form factor by π meson σBcπ in this work varies from 2.42 − 20.7 mb and σBcρ is found to be in the range of 0.72 − 4.6 mb. Thermal average cross-sections of Bc are evaluated with form factor when cut off parameter is 1 and 2 GeV. Using these thermal average cross-sections in kinetic model, time evolution of Bc meson is studied. This model is based on a schematic hydrodynamic description of expanding hadronic matter formed from central Au+Au collision at RHIC. We found that Bc mesons abundance are affected by almost 8% and 11% by final state interaction when cutoff parameter Λ = 1 and 2 GeV, respectively.