Hello @Will Spagnoli ,
Your issue details are not much clear. Have you setup the Bitnami WordPress as an Azure Webapp service? If so, please go thorugh my blog here to understand, how to setup a custom domain for the webapp
http://cloudcompute.info/how-to-configure-an-azure-app-from-marketplace-in-a-custom-domain/
If this is not the case, please let's know more details on the issue
Please mark as "Accept the answer" if the above steps helps you. Others with similar issues can also follow the solution as per your suggestion
Regards,
Manu