If I heat a vertically oriented metal bar at the top would the heat travel to the bottom as fast.....?

If the bar were perfectly insulated from the environment then the orientation of the bar would have no influence on the speed with which things heat up. If the bar is not insulated heat will be lost to the environment, heating up the surrounding air, warm air rises so there might be a difference depending on how the bar is oriented. How big this influence is depends on the setup.