  We study a set of CFT operators suitable for reconstructing a charged bulk
scalar field $\phi$ in AdS${}_3$ (dual to an operator ${\cal O}$ of dimension
$\Delta$ in the CFT) in the presence of a conserved spin-$n$ current in the
CFT. One has to sum a tower of smeared non-primary scalars $\partial_{+}^{m}
J^{(m)}$, where $J^{(m)}$ are primaries with twist $\Delta$ and spin $m$ built
from ${\cal O}$ and the current. The coefficients of these operators can be
fixed by demanding that bulk correlators are well-defined: with a simple ansatz
this requirement allows us to calculate bulk correlators directly from the CFT.
They are built from specific polynomials of the kinematic invariants up to a
freedom to make field redefinitions. To order $1/N$ this procedure captures the
dressing of the bulk scalar field by a radial generalized Wilson line.
