The charge-collection dynamics in poly(3-hexylthiophene:[6,6]-phenyl-C-61-butyric acid methyl ester (P3HT:PCBM) bulk heterojunctions are studied in thick (> 1 mu m) devices using time-of-flight measurements and external quantum-efficiency measurements. The devices show Schottky-diode behavior with a large field-free region in the device. Consequently, electron transport occurs by diffusion in the bulk of the active layer. At high applied biases where the depletion region spans the entire active layer, normal time-of-flight transients are observed from which the electron mobility can be determined. Here, the electron mobility follows Poole-Frenkel behavior as a function of field. At lower applied biases, where the depletion region only spans a small portion of the active layer, due to a high density of dark holes, the recombination kinetics follow a first-order rate law with a rate constant about two orders of magnitude lower than that predicted by Langevin recombination.