Plastic bumper paint touch up

Found a scratch on my back bumper that took off about 4 inches of paint. Probably a parking lot incident. Wondering if this can just be painted over. I don't care what it looks like as long as the scratch is covered and the color is close. What's the best route? The dealership said they'd charge me $10 to swipe the scratch with paint. Am looking for alternatives.

 

I have absolutely no interest in getting this fixed at a body shop. May as well burn the money. It's a scratch on a brand new car. Very annoying, but it's done and time to move on. Just want to cover up the gray of the plastic bumper under the car's paint color. Not interested in a professional paint, buff, cure the paint job. I thought of buying the paint, but figure it would cost more than $10. A touch-up pen is about $12. Maybe I should just invest in that... for future scrapes. I thought since I bought the car new in August that the dealership would just swipe a couple of strokes over the scratch and do it while the car is in for its 5000 checkup. Naw, to easy. They want $10 bucks. Sometimes it's the just the principle of the thing.