Assuming you have a coloured section of the bar to indicate the current amount eg 60%. Then at the top or right end of the 'filled' part of the bar (depending on its orientation), instead of having a straight join to the empty part of the bar you could have an angled join, shaped like a >.
Where ||| denotes filled section and ... denotes empty section. (I'd draw it but I'm on my mobile!)
If the bar is filling you use an arrow pointing into the empty section, but if the bar is emptying, use an arrow pointing into the full section. If the bar is static, use a straight join. You could work out the direction required by averaging change over the most appropriate unit of time, and you could make the acuteness of the arrow point relative to the rate of change.
If you need to bring attention to the bar even more, you could animate the bar in a pulsing fashion such that it animates between a previous position and the current position - again with the previous position being determined by a suitable amount of time. This would emphasise the direction and rate of change.