  We present a study of electrical transport properties of $R$Bi$_2$ ($R$ = La,
Ce) under hydrostatic pressure up to $\sim$ 2.5 GPa. These measurements are
complemented by thermodynamic measurements of the specific heat on CeBi$_2$ at
different pressures up to 2.55 GPa. For CeBi$_2$, we find a moderate increase
of the antiferromagnetic transition, $T_\text N$, from 3.3 K to 4.4 K by
pressures up to 2.55 GPa. Notably, resistance measurements for both CeBi$_2$
and LaBi$_2$ show signatures of superconductivity for pressures above $\sim$
1.7 GPa. However, the absence of superconducting feature in specific heat
measurements for CeBi$_2$ indicates that superconductivity in CeBi$_2$ (and
most likely LaBi$_2$ as well) is not bulk and likely originates from traces of
Bi flux, either on the surface of the plate-like samples, or trapped inside the
sample as laminar inclusions.
