  We provide a theory of triplon dynamics in the valence bond solid ground
state of the coupled spin-ladders modelled for BiCu$_2$PO$_6$. Utilizing the
recent high quality neutron scattering data [Nature Physics (2015), DOI:
10.1038/NPHYS3566] as guides and a theory of interacting triplons via the bond
operator formulation, we determine a minimal spin Hamiltonian for this system.
It is shown that the splitting of the low energy triplon modes and the peculiar
magnetic field dependence of the triplon dispersions can be explained by
including substantial Dzyaloshinskii-Moriya and symmetric anisotropic spin
interactions. Taking into account the interactions between triplons and the
decay of the triplons to the two-triplon continuum via anisotropic spin
interactions, we provide a theoretical picture that can be used to understand
the main features of the recent neutron scattering experimental data.
