  Based on the self-consistent T-matrix approximation (SCTMA), analytical
theory of density of states (DOS) in three-dimensional quantum magnets with the
bond disorder is proposed. It successfully describes DOS in both cases of
resonant and non-resonant scattering which appearance is governed by the ratio
of scattering length and the average distance between impurities. Corrections
to the quasiparticles band gap in these cases are shown to be $\propto c^{2/3}$
and $\propto c$, respectively. Moreover, the theory yields a semi-circle form
of DOS for the bound states inside the gap which results in highly nontrivial
DOS in the intermediate parameters region between two limiting cases when the
band DOS and the semi-circle are overlapped. Long-wavelength excitations are
discussed. In the resonant regime their damping is almost constant $\propto
c^{2/3}$, which according to Ioffe-Regel criterion means their localization.
Applicability of the theory is illustrated by a quantitative description of the
recent experimental data on spin-dimer system Ba$_{3-x}$Sr$_x$Cr$_2$O$_8$.
