The Collaborative International Dictionary of English v.0.48:

bank on \bank on\, v. t.
   Depend on; be confident of.
   [PJC]

Moby Thesaurus II by Grady Ward, 1.0:

35 Moby Thesaurus words for "bank on":
   aspire to, bargain for, bet on, calculate on, confide, count on,
   depend on, desire, expect, feel confident, figure on, gamble on,
   harbor the hope, hope, hope against hope, hope and pray, hope for,
   hope in, hope to God, lean on, lean upon, live in hopes,
   nurture the hope, place reliance on, plan on, presume, reckon on,
   rely on, rely upon, repose on, rest assured, rest on, swear by,
   trust, trust to