  In this Rapid Communication, a set of $^{209}$Bi-nuclear magnetic resonance
(NMR)/nuclear quadrupole resonance (NQR) measurements has been performed to
investigate the physical properties of superconducting (SC) BaTi$_2$Bi$_2$O
from a microscopic point of view. The NMR and NQR spectra at 5~K can be
reproduced with a non-zero in-plane anisotropic parameter $\eta$, indicating
the breaking of the in-plane four-fold symmetry at the Bi site without any
magnetic order, i.e., `the electronic nematic state'. In the SC state, the
nuclear spin-lattice relaxation rate divided by temperature, $1/T_1T$, does not
change even below $T_{\rm c}$, while a clear SC transition was observed with a
diamagnetic signal. This observation can be attributed to the strong
two-dimensionality in BaTi$_2$Bi$_2$O. Comparing the NMR/NQR results among
BaTi$_2$$Pn$$_2$O ($Pn$ = As, Sb, and Bi), it was found that the normal and SC
properties of BaTi$_2$Bi$_2$O were considerably different from those of
BaTi$_2$Sb$_2$O and BaTi$_2$As$_2$O, which might explain the two-dome structure
of $T_{\rm c}$ in this system.
