The conjecture of Bollob\'as and Koml\'os, recently proved by B\"ottcher,
Schacht, and Taraz [Math. Ann. 343(1), 175--205, 2009], implies that for any
γ>0, every balanced bipartite graph on 2n vertices with bounded degree
and sublinear bandwidth appears as a subgraph of any 2n-vertex graph G with
minimum degree (1+γ)n, provided that n is sufficiently large. We show
that this threshold can be cut in half to an essentially best-possible minimum
degree of (21+γ)n when we have the additional structural
information of the host graph G being balanced bipartite. This complements
results of Zhao [to appear in SIAM J. Discrete Math.], as well as Hladk\'y and
Schacht [to appear in SIAM J. Discrete Math.], who determined a corresponding
minimum degree threshold for Kr,s-factors, with r and s fixed.
Moreover, it implies that the set of Hamilton cycles of G is a generating
system for its cycle space.Comment: 16 pages, 2 figure