If you did cause an accident, then contact either your insurance company or the other person. If the damage is minor, then it should be a minor matter. You may retain an attorney to represent you but it may not be cost effective.
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Maybe he saw it or maybe someone else did. You can't stop him from suing you. Under the terms of your auto policy you are suppossed to place your carrier on notice of a possible claim or it can disclaim against you later.
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If he can prove you did it, you are liable for the repair. As has been said, your insurance company will not cover this if you don't timely report it to them. However, if you report it and they pay for repairs, your rates will go up. Obviously, if the cost to repair is less than your deductible, reporting it can be counterproductive. You should call this person and see what evidence they have that you did this and then you can make a better informed decision. Also, take and preserve photos of your own bumper if it shows no damage.