We calculate the total inclusive ($p, {\ensuremath{\pi}}^{\ensuremath{-}}\mathrm{xn}$) reaction cross section for 200 MeV protons on $^{209}\mathrm{Bi}$ using a simplified intranuclear cascade model in which only one particle at a time is tracked through the nucleus. Computer time is kept to a minimum by multiplying the very small $\mathrm{NN}\ensuremath{\rightarrow}\mathrm{NN}\ensuremath{\pi}$ probability by a weighting factor. The nucleon and pion charge exchange mechanisms contribute more than half the cross section. The predictions are sensitive to choice of energy in the $\mathrm{NN}\ensuremath{\rightarrow}\mathrm{NN}\ensuremath{\pi}$ input cross sections, but a reasonable choice gives cross sections in agreement with experiment. The predicted ($p, {\ensuremath{\pi}}^{\ensuremath{-}}\mathrm{xn}$) cross section grows rapidly from ${T}_{\mathrm{lab}}=160$ MeV (just above threshold) to 220 MeV.NUCLEAR REACTIONS $^{209}\mathrm{Bi}(p, {\ensuremath{\pi}}^{\ensuremath{-}}xn)^{210\ensuremath{-}x}\mathrm{At}$, $E$ near 200 MeV, calculated $\ensuremath{\sigma}(E)$, simplified intranuclear cascade model, nucleon and pion charge exchange.