Looks good, but you don't need any lists!
A method would just take in the parameters and perform the checks on them. You know the amount of an item by getInventory().getAmount() - make sure you have some though, otherwise this will throw an error.
This should get you started, wrote it in reply box so apologies if there are any errors!
private boolean withdrawItem(String itemName, int amount, boolean noted, boolean stackable) {
if (!stackable && amount>28) return false; // illegal argument
if (getBank().isOpen()) { // make sure bank is open
int currentAmount = getInventory().contains(itemName) ? getInventory().getAmoumt(itemName) : 0;
int amountNeeded = amount - currentAmount;
if (amountNeeded > 0) {
// Withdraw some!
} else if (amountNeeded < 0) {
// Deposit some!
} else return true; // We already have the right amount!
} else return false;
}