  We present a detailed nuclear magnetic resonance (NMR) study of ${}^{239}$Pu
in bulk and powdered single-crystal plutonium tetraboride (PuB$_4$), which has
recently been investigated as a potential correlated topological insulator.
This study constitutes the second-ever observation of the ${}^{239}$Pu NMR
signal, and provides unique on-site sensitivity to the rich $f$-electron
physics and insight into the bulk gap-like behavior in PuB$_4$. The
${}^{239}$Pu NMR spectra are consistent with axial symmetry of the shift tensor
showing for the first time that ${}^{239}$Pu NMR can be observed in an
anisotropic environment and up to room temperature. The temperature dependence
of the ${}^{239}$Pu shift, combined with a relatively long spin-lattice
relaxation time ($T_1$), indicate that PuB$_4$ adopts a non-magnetic state with
gap-like behavior consistent with our density functional theory (DFT)
calculations. The temperature dependencies of the NMR Knight shift and
$T_1^{-1}$--microscopic quantities sensitive only to bulk states--imply bulk
gap-like behavior confirming that PuB$_4$ is a good candidate topological
insulator. The large contrast between the ${}^{239}$Pu orbital shifts in the
ionic insulator PuO$_2$ ($\sim$~+24.7~\%) and PuB$_4$ ($\sim$~-0.5~\%) provides
a new tool to investigate the nature of chemical bonding in plutonium
materials.
