Quote:
I have found that the mails which get bounced to the root's mailbox are mostly undelivered mails due to some reason.
This part of your problem is not a problem - it's suppose to do this. If you check your aliases file, postmaster is probably set up to go to root. It has to be going to someone. You could have it go to your account.
RFC 822 - Aliases required by the mail protocol
postmaster: root
MAILER-DAEMON: postmaster
You can change it, but it has to go to a person so errors in your configurations will be known and can be fixed.
If your 'users' are sending to dead addresses in such quanitity that it's overwhelming you, you may want to talk to your 'users'. It may be they are spamming...