Bouncing on the other end has nothing to do with running your own mail domain. In e-mail, sending and receiving are decoupled. Some people use the same local mail server to do both: to relay outgoing mail and to receive. But these are independent functions, and you don't have to send mail through your server. You can configure your mail client(s) with the SMTP credentials from you mail provider (such as your ISP). That's used for sending. For receiving, you connect to your own server via IMAP4.

Basically your sending side (if you choose to) can be essentially unrelated to your self-hosted mail receiving infrastructure except in the small fact of using your sending identity in the From: headers of your e-mails: [email protected].