Default Billing Email

I have several contacts with one company that would like to receive the emails to one email address. for example. billing@company.com  The contact is with a company and his email is contact@company.com

The blue arrow will only send the invoice to the client default email. The client default email blue arrow is used for the quote and is not always the bill to email. 

Sales will email the default client email the quote. This client is inherited into the invoice as it is the only option for the email template outside of vendor.  Bill To does not have an option to select a email template nor does it any workflow job allow you to select a bill to email.

I would like a default bill to email option added to the contact under the internet tab and the ability to add this string to a workflow job OR I would like the Bill To Contact Associations to have a Email Template option.