I support Magento enterprise at my day job and have personally applied numerous patches successfully.
If the site in an enterprise site, I will need access to download the patch along with the patch name (SUPEE-??) or you will need to provide me with the patch directly. Additionally, I will need command-line access to the web server with enough access to apply the patch.
I recommend taking a backup of not only the site's source code, but the database as well, prior to the patching being installed. I also recommend testing the patch on a clone of the website prior to applying the patch to a live site. Lastly, I recommend having a test routine documented to that the success of the patch can be tested.
I can assist with with backing up the site's source code and applying it to a clone, but I will not be able to create a clone, apply the patch to more than 1 live site and 1 clone, run the test routines before and after the application of the patch, nor revert the patch if necessary for the bid price. With that said, I will be more than happy to coordinate those efforts with you during a predetermined deployment time frame.