  We study a bilayer of the frustrated $J_1$-$J_2$ Heisenberg-model on the
square lattice. Starting from the dimer limit at strong interlayer coupling, we
perform series expansions using the perturbative Continuous Unitary
Transformation, based on the flow equation method, in order to determine the
spectrum up to the two-triplon sector. From the one-triplon dispersion we
obtain quantum critical lines for transitions from the dimer phase into either
N\'eel or collinear magnetic order. For low to intermediate frustration these
transitions are consistent with existing findings, based on the magnetic
phases. In the region of strongest frustration, i.e. $J_2/J_1\sim 0.5$, we
provide an estimate for the stability of the anticipated single-layer quantum
spin-liquids against finite interlayer coupling. In the two-triplon sector we
find a set of well defined (anti)bound states, which can be classified
according to total spin and in-plane rotational symmetry. For vanishing
frustration these states agree with previous series expansion analysis. For
$J_2/J_1\gtrsim 0.5$ we provide evidence for a close-by condensation of
one-triplon and two-triplon singlet bound states, suggesting that between the
dimer and the collinear state, additional phases may intervene.
