Banking on something means to rely or depend on it. If you want to switch up your vocabulary, there are plenty of synonyms for "bank on" that you can use in your writing or conversation. Some alternatives include "count on," "depend on," "rely on," "trust in," "bet on," "have faith in," "lean on," "believe in," "pin your hopes on," "put your money on," and "rest assured in." These different phrases can lend a different tone or emphasis to your statements, and can add some variety to your language.