We present a study of electrical transport properties of RBi2 (R=La,Ce) under hydrostatic pressure up to ∼2.5 GPa. These measurements are complemented by thermodynamic measurements of the specific heat on CeBi2 at different pressures up to 2.55 GPa. For CeBi2, we find a moderate increase of the antiferromagnetic transition, TN, from 3.3 K to 4.4 K by pressures up to 2.55 GPa. Notably, resistance measurements for both CeBi2 and LaBi2 show signatures of superconductivity for pressures above ∼1.7 GPa. However, the absence of superconducting features in specific-heat measurements for CeBi2 indicates that superconductivity in CeBi2 (and most likely LaBi2 as well) is not bulk and likely originates from traces of Bi flux, either on the surface of the platelike samples, or trapped inside the sample as laminar inclusions. Finally, we point out that extra caution should be exercised when claiming superconductivity based just on transport measurements, especially for Bi-containing compounds.