If you have IMAP enabled on your Zimbra server, you can set up a BIS connection through your wireless provider. The details for how to get there vary by provider, but can be found here
BlackBerry - BlackBerry Smartphone and Email Account Setup
If you want full email+calendar sync and have the mobile add-on for your Zimbra installation, you would still need to setup a server running Blackberry Enterprise Server (BES) for the Zimbra Connector for Blackberry (ZCB) to work. Phoenix's link are the details you need to get that going.