We investigated the intermetallic single-crystal superconductor NiBi3 using high-pressure electrical resistivity and specific heat measurements. The application of pressure results in a monotonic decrease of the superconducting transition temperature. While the zero-field specific heat and the magnetic field dependence of the Sommerfeld coefficient indicate an isotropic S-wave gap, the temperature dependence of the upper critical field suggests a slightly anisotropic, fully gapped order parameter. Collectively, these results indicate that the pairing mechanism in NiBi3 is consistent with conventional, electron-phonon-mediated BCS superconductivity.