We report our experimental and theoretical studies on generation and time-resolved detection of coherent acoustic phonons (CAPs) in bulk GaN single crystals, using the femtosecond optical pump-probe spectroscopy. A train of 100-fs-wide, ultraviolet laser pump pulses with the photon energy far above of the GaN bandgap induced electronic stress at the crystal surface and triggered propagation of CAP oscillations. Subsequently, time-delayed, low-intensity, 100-fs-wide, ultraviolet/infrared (one/two-colour setup) probe pulses monitored CAP propagation either near the surface or deeply inside the GaN crystal. The amplitude of CAP oscillations was on the order of 10-5-10-6 of the probe-beam transient differential reflectivity signal, and was only dependent on the pump-beam absorption coefficient. The CAP oscillation frequency was dispersionless (proportional to the probe-beam wave vector) with the slope corresponding to 8000 m/s-the speed of sound in GaN. In our two-colour arrangement, we could detect CAP oscillations as deeply as ~0.1 mm inside the crystal (the pump-probe delay ~13.2 ns), since the CAP signal attenuation was only limited by the absorption of the infrared probe light in GaN. The latter indicated that the intrinsic CAP lifetime in our crystals was actually ultra long and was estimated to be of the order of at least 100 ns.