I don't remember the rules explicitly stating this, but it seems like the only appropriate way to spend CP on movement is one at a time (ie. if I make it 4 squares, I might go further), because the duel to interrupt rules could lead to an interposing opponent that would cut the active player off from his intended route.
There is a case where you might want to spend all CP on movement in one go; If the character were to become injured along the way, you get to use the uninjured movement rate for the entire movement as well as the max cp per turn. If you spend the CP on movement one at a time, your character may not go the same distance. (See page 15 bottom).