A "0" bounce count is what you want!!! It means that all of your sent mailings made it into an inbox!
Before an email can reach someone's inbox, it has to be accepted by the host server. Bounces occur when the SMTP transaction between our mail server and your recipient’s mail server fails.
The error codes given at the time of might be standardized at each organization, but they can be quite different from provider to provider.
There are two main categories for bounces:
Soft bounce (a three-digit response code starting with a 4) – A temporary failure due to an outage, full mailbox or other issue that should resolve itself. Soft bounces are considered temporary, so delivery is reattempted over a 30-hour period before giving up on reaching the receiving server. This can happen for four mailings in a row before we will move the address from Active to Error.
Hard bounce (a three-digit response code starting with a 5) – A permanent obstruction to email delivery, such as a nonexistent email address, a block due to a content or the server is rejecting your email as junk mail. Hard bounces are deemed invalid and moved to Error status. They won't be emailed to again unless you re-activate them.