There have been several changes to the new banking system. The first you will notice when you say bank or click on the banker is the new menu that pops up. You can also click on the banker to open both your bank vault and menu. By clicking on the menu it will close.
The character transfer account is used when you want to move funds from one shard to another. This is the same as using checks. Deposit gold/platinum will put the funds in the account. Use Withdraw gold/platinum to retrieve the funds. As far as I know, this has no use on Heritage.
The secure account is only used to put funds in the new house vault.
When you ask for your balance, the amount of money you have in your secure account
will show up as escrow.
How do I put money in the bank, get it out and find my balance?
You put money in the bank the old way. But when you drop it in, it will disappear, and the amount will be added to Total Gold.
To find the balance, say balance. The banker will then tell you your gold/platinum balance, To remove money say withdraw and the amount.
How do I give another person gold or any other object
Click on the player to get the menu. Click on trade.
This will open up the trade gump again. You can either place the gold in the trade window or you put in the amount. As before both need to click on the blue gem from the transaction to go through.
You can also enable Large bank vault in Options have have a MUCH bigger banking window!
Source: Stratics (Slightly Modified)