We report on the effects of screening of the electric field by doping-induced mobile charges on photocurrent collection in operational organic solar cells. Charge transport and recombination were studied using double injection (DI) and charge extraction by linearly increasing voltage (CELIV) transient techniques in bulk-heterojunction solar cells made from acceptor-donor blends of poly(3-n-hexylthiophene):phenyl-C61-butyric acid methyl ester (P3HT:PC60BM). It is shown that the screening of the built-in field in operational solar cells can be controlled by an external voltage while the influence on charge transport and recombination is measured. An analytical theory to extract the bimolecular recombination coefficient as a function of electric field from the injection current is also reported. The results demonstrate that the suppressed (non-Langevin) bimolecular recombination rate and charge collection are not strongly affected by native doping levels in this materials combination. Hence, it is not necessary to reduce the level of doping further to improve the device performance of P3HT-based solar cells.