  Our current understanding of the core-collapse supernova explosion mechanism
is incomplete, with multiple viable models for how the initial shock wave might
be energized enough to lead to a successful explosion. Detection of a
gravitational-wave signal emitted in the initial few seconds after stellar
core-collapse would provide unique and crucial insight into this process. With
the Advanced LIGO and Advanced Virgo detectors expected to approach their
design sensitivities soon, we could potentially detect this signal from a
supernova within our galaxy. In anticipation of such a scenario, we study how
well the BayesWave algorithm can recover the gravitational-wave signal from
core-collapse supernova models in simulated advanced detector noise, and
optimize its ability to accurately reconstruct the signal waveforms. We find
that BayesWave can confidently reconstruct the signal from a range of supernova
explosion models in Advanced LIGO-Virgo for network signal-to-noise ratios
$\gtrsim 30$, reaching maximum reconstruction accuracies of $\sim 90\%$ at SNR
$\sim 100$. For low SNR signals that are not confidently recovered, our
optimization efforts result in gains in reconstruction accuracy of up to
$20-40\%$, with typical gains of $\sim 10\%$.
