  We examine the evolution of a closed, homogeneous and anisotropic cosmology
subject to a variation of the fine structure 'constant', \alpha, within the
context of the theory introduced by Bekenstein, Sandvik, Barrow and Magueijo,
which generalises Maxwell's equations and general relativity. The variation of
\alpha permits an effective ghost scalar field, whose negative energy density
becomes dominant at small length scales, leading to a bouncing cosmology. A
thermodynamically motivated coupling which describes energy exchange between
the effective ghost field and the radiation field leads to an expanding,
isotropizing sequence of bounces. In the absence of entropy production we also
find solutions with stable anisotropic oscillations around a static universe.
