Hi Kleinandsheridan,
The e-mails might bounce back to the account due to the following reason.
A. The user is not assigned Exchange online license
Assign license.
1. Login to the Admin Page in office 365.
2. Select "Users" under "Management"
3. Select the user you want to edit and assign the Exchange Online license in the Assign Page
Please find the help article related to “Manage licenses”:
http://onlinehelp.microsoft.com/en-in/office365-enterprises/gg570315.aspx
B. The MX record is incorrectly set up.
If the issue persists after assigning the license, I suggest you to check the “MX record”. The “Mx record” configures e-mail routing.
1. Go to the admin page in office 365.
2. Select "Domain" under "Management".
3. Select the domain click "View DNS Setting”, create the DNS records at your DNS hosting provider using the given information for exchange online.
Please find “add records to configure your domain for Exchange Online” in the below link related to” add the DNS record”
http://onlinehelp.microsoft.com/en-in/office365-enterprises/jj655360.aspx
Thanks,
Archana