  Under the assumption that the base field k has characteristic 0, we compute
the algebraic cobordism fundamental classes of a family of Schubert varieties
isomorphic to full and symplectic flag bundles. We use this computation to
prove a formula for the push-forward class of the Bott-Samelson resolutions
associated to the symplectic flag bundle. We specialise our formula to
connective K-theory and the Grothendieck ring of vector bundles, hence
obtaining a description for all Schubert classes.
