This is speculation, but since it goes on like spray paint, I don't see why a small area couldn't be "patched up"; however, I think the question would be whether a shop will be willing to only charge you for that small area. After it's sprayed, they have to bake it in an oven, so they may want to charge you for the whole bumper since they have to handle it and it takes up space in their oven.
Also, another consideration with the powder coat would be its age, as it does fade over time.
Having said that, you may want to look into cans of spray paint in the same color and finish (e.g. rustoleum or krylon) and see if you can touch up the small area to your satisfaction. If not, it would be cheaper to respray the whole bumper.