  Following work of Musta\c{t}\u{a} and Bitoun we recently developed a notion
of Bernstein-Sato roots for arbitrary ideals, which is a prime characteristic
analogue for the roots of the Bernstein-Sato polynomial. Here we prove that for
monomial ideals the roots of the Bernstein-Sato polynomial (over $\mathbb{C}$)
agree with the Bernstein-Sato roots of the mod-$p$ reductions of the ideal for
$p$ large enough. We regard this as evidence that the characteristic-$p$ notion
of Bernstein-Sato root is reasonable.
