Some e-mails to my new address are Bouncing back

Some e-mails to my new address are Bouncing back

E-mails to me are bouncing, but not all of them. Is this just because we've only set up our account today and it takes some time for the server to recognise everything? We have two user accounts and both are receiving some emails and some are bouncing. We've just signed up and paid, so I don't want this to be a continuing issue.