Instructions
Ask a friend from the faction you wish to transfer the money to if he can help you transfer money from the Alliance to Horde or vice versa. Tell your friend to meet you at a neutral auction house, such as the auction house in Ratchet or Booty Bay.
Hand your friend an item that's worthless to you, such as a level 5 common sword. Instruct your friend to list the item on the auction house and to enter the amount of gold you wish to transfer in the "Buyout" box.
Switch to the other faction and the character you're transferring the money from. Visit a neutral auction house and look for the auction your friend just posted. Click on the auction and click "Buyout."
Logon to your other character and wait one hour, which is how long it takes for the money to appear in your friend's mailbox. Ask your friend to trade you the gold.