A bifurcative step transition from low-density, high-temperature, attached divertor conditions to high-density, low-temperature, detached divertor conditions is experimentally observed in DIII-D tokamak plasmas as density is increased. The step transition is only observed in the high confinement mode and only when the B× B drift is directed towards the divertor. This work reports for the first time a theoretical explanation and numerical simulations that qualitatively reproduce this bifurcation and its dependence on the toroidal field direction. According to the model, the bifurcation is primarily driven by the interdependence of the E×B-drift fluxes, divertor electric potential structure, and divertor conditions. In the attached conditions, strong potential gradients in the low field side (LFS) divertor drive E×B-drift flux towards the high field side divertor, reinforcing low density, high temperature conditions in the LFS divertor leg. At the onset of detachment, reduction in the potential gradients in the LFS divertor leg reduce the E×B-drift flux as well, such that the divertor plasma evolves nonlinearly to high density, strongly detached conditions. Experimental estimates of the E×B-drift fluxes, based on divertor Thomson scattering measurements, and their dependence on the divertor conditions are qualitatively consistent with the numerical predictions. The implications for divertor power exhaust and detachment control in the next step fusion devices are discussed.