We have investigated the dynamical properties of the coherent anharmonic phonons generated in Bi under high density excitation. The time-resolved reflectivity in the intensely photoexcited Bi film is modulated by the coherent A(1g) phonon oscillation with a time-dependent oscillation period. As the pump power density is increased, the line shape of the A(1g) mode in the Fourier transformed spectra becomes asymmetric, and the redshift of the phonon frequency is observed. Analysis of the transient redshift with a wavelet transform reveals that the frequency of the A(1g) mode depends on the squared amplitude of the oscillation, which is attributed to an anharmonicity of the lattice potential.