Haven't setup anything to auth to zimbra but hopefully whatever follows might help:
In my case, I'm using external auth from zimbra, to an external openldap server via ldap/tls (port 389 w/ TLS). I chose that setup since I didn't want to bother with adding the ldap cert into zimbra's java keystore. Since I went with TLS, I don't need to bind as an account.
The UI I see you posted doesn't explicitly say anything about encryption - maybe it does TLS in the background, in an effort to hide details from you. Or maybe it's in that dropdown. I'm guessing by default zimbra would require some sort of encryption (LDAP w/ tls or LDAPS).
If you think you need to bind as a user try the whole distinguished name:
uid=zimbra,cn=admins,cn=zimbra
Here's how you'd set it's password if you don't know it:
Setting zimbra admin password in LDAP - Zimbra :: Wiki
Also, you might want to look up how people are auth'ing samba (or whatever else) against Zimbra, or whatever else against zimbra.
It might help others to help you if you mention the software - my google-skillz say you're using ServiceDesk Plus:
Configuring LDAP authentication