  We study $\mathcal{O}$-operators of associative conformal algebras with
respect to conformal bimodules. As natural generalizations of
$\mathcal{O}$-operators and dendriform conformal algebras, we introduce the
notions of twisted Rota-Baxter operators and conformal NS-algebras. We show
that twisted Rota-Baxter operators give rise to conformal NS-algebras, the same
as $\mathcal{O}$-operators induce dendriform conformal algebras. And we
introduce a conformal analog of associative Nijenhius operators and enumerate
main properties. By using derived bracket construction of Kosmann-Schwarzbach
and a method of Uchino, we obtain a graded Lie algebra whose Maurer-Cartan
elements are given by $\mathcal{O}$-operators. This allows us to construct
cohomology of $\mathcal{O}$-operators. This cohomology can be seen as the
Hochschild cohomology of an associative conformal algebra with coefficients in
a suitable conformal bimodule.
