Go to the bank, open your account, click Deposit. On the pop-up there is a tiny box where you can set the amount of gold to deposit. There will be depositing fees, however, which are stated in the box. The fees will not be deposited into the bank and is instead taken away from you. The more gold you have in the bank, the higher the fees rate.
The fees charged is calculated by multiplying the depositing amount by the fees rate (in percentage).
The maximum fees rate is 10% of the depositing amount.
Taking out a check
Go to the bank, open your account, click Withdrawal. On the pop-up there is a tiny box you can check next to Issue a Check. Click that if you want to send a lump sum of money to an individual in the game or a guild (at the guild marker). Note, if you send checks by mail there will be a mail fee of at least 50 gold. The minumum size check you can issue is 10,000g and checks can only be written in 10,000g increments.
The processing fee is 5% of the amount the check is written for.
If you take out a 10,000g check, the process fee is 500g
If you take out 100,000g check, the process fee is 5000g.