You can only send a private message to Bin Weevils that are on your Buddy List. To do so, click on the Bin Buddy Messenger buddy you wish to send a message to, click on the envelope and type a message.
You can also select the buddy from your Buddy List if they are not online. Your message will be sent to their mailbox, and they will see it when they come back to their nest. Remember, all messages on Bin Weevils are being watched by moderators!