1
general::
Phrase(s): bank on something
Fig. to be so sure of something that one can trust it as one might trust a bank with one’s money. • I will be there on time. You can bank on it. • I need a promise of your help. I hope I can bank on it.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Rely on, count on. For example, You can bank on Molly's caterer to do a good job. This expression alludes to bank as a reliable storage place for money. [Late 1800s]
American Heritage Idioms