the Bank changes every 24 hours, but follows a pattern: Starts around 350 coins per Bux. After a few days, it changes to roughly 250 coins per Bux, and then changes to 150 (or even 100) coins per Bux. It then resets back to roughly 350 coins per Bux.
If the player presses the back arrow on the Bux input area, it will show 0 Bux to 0 Coins. You have to have 0 Bux for this to work.