The username (in AB.app) needs to be the left side of your email address, e.g. for
bob@somedomain.com you enter only 'bob'. Server address needs to be the FQDN associated with you email address domain, and you need to append :80 or :443 (as required) to the FQDN, e.g. mail.somedomain.com:80 else AB.app will attempt to connect on port 8800 (default for OSX Server). That works for me.
Do you have calendar access? ..I have a vague recollection that unless you have calendar (and thus CalDAV) in your COS, you don't get WebDAV access to your mailbox, and CardDAV requires it.