Black phosphorus (BP) has emerged as a direct-bandgap semiconducting material with great application potentials in electronics, photonics, and energy conversion. Experimental characterization of the anisotropic thermal properties of BP, however, is extremely challenging due to the lack of reliable and accurate measurement techniques to characterize anisotropic samples that are micrometers in size. Here, we report measurement results of the anisotropic thermal conductivity of bulk BP along three primary crystalline orientations, using the novel time-resolved magneto-optical Kerr effect (TR-MOKE) with enhanced measurement sensitivities. Two-dimensional beam-offset TR-MOKE signals from BP flakes yield the thermal conductivity along the zigzag crystalline direction to be 84 ~ 101 W/(m*K), nearly three times as large as that along the armchair direction (26 ~ 36 W/(m*K)). The through-plane thermal conductivity of BP ranges from 4.3 to 5.5 W/(m*K). The first-principles calculation was performed for the first time to predict the phonon transport in BP both along the in-plane zigzag and armchair directions and along the through-plane direction. This work successfully unveiled the fundamental mechanisms of anisotropic thermal transport along the three crystalline directions in bulk BP, as demonstrated by the excellent agreement between our first-principles-based theoretical predictions and experimental characterizations on the anisotropic thermal conductivities of bulk BP.