  Let $\rm{Bun}$ be the moduli stack of rank $2$ bundles with fixed determinant
on a smooth proper curve $C$ over a local field $F$. We show how to associate
with a Schwartz $\kappa$-density, for $\rm{Re}(\kappa)\ge 1/2$, a smooth
function on the corresponding coarse moduli space of very stable bundles. In
the non-archimedean case we also prove that the stack $\rm{Bun}$ is
$\kappa$-bounded in the sense of Definition 2.10 of [arXiv:2112.08139] for any
$\kappa\in\mathbb{C}$.
