The Bernstein-Sato Polynomial is a classical \(D\)-module invariant that has been used to measure the singularities of a hypersurface \(f\). In this talk we will review some of the classical theory before considering the Bernstein-Sato polynomial over a numerical semigroup ring \(R\). We will see that in this case the Bernstein-Sato polynomial detects not just of an element in \(R\) but of the ambient numerical semigroup ring itself.