You should check out Private Browsing. Nothing you do in a Private Browsing window is stored on your computer once you close that window, including history, cookies, information entered in forms, and anything which would normally be cached by Firefox.

Also, could you clarify what you mean by "saving bank account data"? Here are some places that Firefox may save data you have viewed:

Firefox's cache: Generally speaking, Firefox will cache pages you have viewed so you can go Back to them unless the server instructs Firefox not to store them, or designs the page to reload and check to make sure you are still logged in.

Session history: Firefox saves information about your session for purposes of redisplaying your open windows and tabs (and recently closed windows and tabs) in the event of a crash. If you want to restrict what Firefox saves, there might be some settings you can modify, but it depends on your concerns.

Form autofill: If you have the form fill feature enabled, Firefox will remember data you enter into forms (usually excluding passwords). This can be turned off, or completely cleared, but there isn't a convenient way to remove just some of the data without an add-on. For example: https://addons.mozilla.org/firefox/addon/form-history-control/