Reference.SetAnimationVariableBool("bAnimationDriven", true)
will cause "moveStart" to actually move you forward. It will also make "SprintStart" to move the actor forward, too. Usually calling "SprintStart" will cause the actor to sprint in place, but setting the actor into an "Animation Driven" (as opposed to the default "Motion Driven") state will mean the animations determine what the actor does, not it's motion, thus causing him to run forward.
Link to all animation variables: http://www.gamesas.com/topic/1360112-full-dump-of-all-animation-variables/