  The addition of non-renormalizable terms involving the Higgs fields to the
MSSM (BMSSM) ameliorates the little hierarchy problem of the MSSM. We analyze
in detail the two main cosmological issues affected by the BMSSM: dark matter
and baryogenesis. The regions for which the relic abundance of the LSP is
consistent with WMAP and collider constraints are identified, showing that the
bulk region and other previously excluded regions are now permitted. Requiring
vacuum stability limits the allowed regions. Based on a two-loop finite
temperature effective potential analysis, we show that the electroweak phase
transition can be sufficiently first order in regions that for the MSSM are
incompatible with the LEP Higgs mass bound, including parameter values of
\tan\beta \lsim 5, m_{\tilde{t}_{1}} > m_t, m_Q << TeV.
