Pulled original file version ofapp/design/frontend/enterprise/default/template/persistent/checkout/onepage/billing.phtml
and placed in directory.
Moved modified core file to template override directory.
One thing to note in order to retain the security changes for the template over ride file, I had to manually make the changes to the template file version directly.
Example of moving core file to template override directory:
app/design/frontend/enterprise/default/template/persistent/checkout/onepage/billing.phtml moved too app/design/frontend/YOUR_TEMPLATE/YOUR_TEMPLATE/template/persistent/checkout/onepage/billing.phtml
Installed patch- success
Hope this helps someone else out there.
Answer credit goes toRaphael at Digital Pianism as his answer is correct and placed here before mine, just wanted to provide a step by step of what I did to successfully install the patch.