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Buy a new bumper or used one. Spend some more money on the tools you may need to fix it. If you have some tools that is great.
But what you will learn by repairing it yourself is invaluable. I have been trying to fix whatever I could myself since my first car. I always ended up running out in the middle of a job to get a new tool, because what I was trying to accomplish was too difficult with what tools I already owned. 22 years later I have a garage full of tools and can tackle almost anything except straightening a chassis or lifting the car up 7 feet to work on it. DO IT YOURSELF.
If you only master changing the oil that is fine also. If you change the oil in your parents car and save them a few bucks a year; maybe they will forgive you.
There shouldn't even be a discussion - be a man and tell them what happened.
Throughout your life there's going to be plenty of opportunities to either stand by your actions (and mistakes) or bury your head in the sand. Get a head start on doing the right thing. It may be cheaper to lie or otherwise maneuver your way out, but integrity is priceless.