Using path-integral Monte Carlo and the maximum entropy method, we calculate the dynamic structure factor of solid 4He in the bcc phase at a finite temperature. Both the single-phonon contribution to the dynamic structure factor and the total dynamic structure factor are evaluated. From the dynamic structure factor, we obtain the phonon dispersion relations along the main crystalline directions, [001], [011], and [111]. We calculate both the longitudinal and transverse phonon branches. We discuss the differences between dispersion relations resulting from the single-phonon part versus the...