We perform a comprehensive analysis of the dynamical magnetic susceptibility χ(q, ω) in the slave-boson mean-field scheme of the bilayer t-J model. We use model parameters appropriate for YBa 2 Cu 3 O 6+x (YBCO), a typical bilayer high-T c cuprate compound well studied by neutron scattering experiments. In the d-wave pairing state, the strongest magnetic spectral weight appears at q = Q ≡ (π, π) and ω = ω res Q , and spreads into a diamond-shaped shell around Q in q space for ω < ω res Q . This weight is due to a collective mode, namely a particle-hole bound state, which has a downward ω versus q dispersion around Q. Within the high intensity shell, the incommensurate (IC) signals at q = (π, π ± 2πη) and (π ± 2πη, π) tend to be stronger than the diagonal incommensurate (DIC) signals at q = (π ± 2πη ′ , π ± 2πη ′ ), especially for a large hole density δ. For ω ≪ ω res Q the IC signals completely disappear and the weight remains only around the DIC positions. For ω > ω res Q strong signals of Imχ(q, ω) tracing an upward dispersion are found and interpreted as an overdamped collective mode near ω res Q . In the normal state, Imχ(q, ω) has a broad peak at q = Q. That is, the IC and DIC signals appear only in the dwave pairing state. We also study effects of a small orthorhombic anisotropy, which is intrinsic in untwinned YBCO crystals. Because of electron-electron correlations favoring d-wave shaped Fermi surface deformations (dFSD), we expect an enhanced anisotropy of magnetic excitation spectra. This effect is particularly pronounced for low δ and at relatively high temperature. The present theory provides a rather detailed microscopic explanation of the most salient properties of magnetic excitations observed in YBCO.