Why does the base need to be biased as well?

For normal transistor operation, there needs to be forward bias from the base to the emitter (in the direction of the pn ``diode'')-- in fact this is critical for operation of the transistor. This bias makes the emitter less positive, counteracting the effect of the diffusion-created depletion region (in fact the depletion region can completely go away). Electrons from the emitter are then able to drift towards the collector (attracted by the positive voltage on the collector side), creating the current $I_C\sim I_E$ (which is in the direction of positive charge flow, so opposite to the direction of travel of the electrons).