Ferroelectric tungsten-based Aurivillius oxides are naturally stable superlattice structures, in which $A$-site deficient perovskite blocks ${[{\mathrm{W}}_{n}{\mathrm{O}}_{3n+1}]}^{\ensuremath{-}2}$ ($n=1,2,3,\ensuremath{\cdots}$) interleave with fluorite-like bismuth oxide layers ${[{\mathrm{Bi}}_{2}{\mathrm{O}}_{2}]}^{+2}$ along the $c$-axis. In the $n=2\phantom{\rule{4pt}{0ex}}{\mathrm{Bi}}_{2}{\mathrm{W}}_{2}{\mathrm{O}}_{9}$ phase, an in-plane antipolar distortion dominates but there has been controversy as to the ground-state symmetry. Here we show, using a combination of first-principles density functional theory calculations and experiments, that the ground state is a nonpolar phase of $Pnab$ symmetry. We explore the energetics of metastable phases and the potential for antiferroelectricity in this $n=2$ Aurivillius phase.