The dynamic magnetic behaviors of the spin-1 Blume-Capel Ising bilayer system (BCIS) are studied in an oscillating external magnetic field on a two-layer square lattice by utilizing the mean field theory (MFT) based on Glauber-type stochastic dynamics [dynamic mean field theory (DMFT)]. The dynamic equations describing the time-dependencies of the average magnetizations are obtained with the Master equation. The dynamic phases in this system are found by solving these dynamic equations. The temperature dependence of the dynamic order parameters is examined to characterize the nature (continuous or discontinuous) of the phase transitions and to obtain the dynamic phase transition (DPT) points. The dynamic phase diagrams (DPDs) are shown for ferromagnetic/ferromagnetic, antiferromagnetic/ferromagnetic, antiferromagnetic/antiferromagnetic interactions in the plane of the reduced temperature versus magnetic field amplitude and they display dynamic tricritical and re-entrant behavior as well as the dynamic triple point (tp).