I manage a Google Apps domain with about ten users on it. Only one of the users is a really heavy email user and is about to fill up her email quota. I would like to find a way to add extra quota to that user. The only information I can find from the Google help is that I must upgrade all the users to the business edition. Is there any way that I can just buy some more quota for a single user?
No you can't do that and you will have to upgrade to the Google Apps for Business in order to get more space.
From the FAQ for Google Apps:
Can I have a subset of employees on Google Apps for Business and others on Google Apps?
Google Apps does not support Google Apps and Google Apps for Business user accounts as part of the same organization's Google Apps account.