The Bill of Rights is itself based on natural law.
The Bill of Rights protects certain rights. What those rights are based on is not important; the point is that they are protected. Thus, whether these rights are natural, or are granted by some divine being, or are simply arbitrary creations of mankind, is irrelevant.
But the very idea that certain guarantees mentioned in the Bill of Rights are "natural" is absurd. The Seventh Amendment, for example, requires trial by jury in civil cases where the amount in controversy is more than $20. I fail to see anything "natural" about the twenty dollar rule.