If you have a BU Google Apps account and decide that you would like to set up forwarding from the BU Google Mail component to an external mail service, even if that other service is commercial Gmail, you should use the BU Google Mail Settings->Forwarding and POP/IMAP interface to set up forwarding of your mail from BU Google Mail to the external account.
You can access Mail Settings, from the “gear” icon in the upper right corner of BU Google Mail. For details, follow the steps described in the related Google article. Note that, even after you have set up forwarding of mail, you will still have your BU Google Apps account and are still welcome to use the other associated applications, such as Drive, Sites or Calendar.