  We present spectroscopy and photometry of the LMC supersoft binary system
RX~J0513.9-6951. We derive a refined spectroscopic period of
P$=0.761\pm0.004$~d, which is consistent with the value obtained from long term
photometric monitoring (P$=0.76278\pm0.00005$~d). We see bipolar outflow
components of He{\sc ii} and H$\beta$, with velocities of $\sim
3800$\,km\,s$^{-1}$, strongly suggesting that the compact object is a white
dwarf. Using all the available optical and X-ray data, we construct a
theoretical model to explain the principal features of the unusual variability
of this source. In particular, we note that X-ray outbursts have only been seen
at times of optical minima. From this, we conclude that the most likely cause
of the X-ray outbursts is a photospheric contraction during a nuclear shell
burning phase, rather than a thermonuclear flash or shocked emission. The
system probably comprises a relatively massive white dwarf accreting at a high
rate ($\sim 10^{-6} M_{\odot}~{\rm yr}^{-1}$) from an evolved donor star, and
is observed close to pole-on.
