I know, not much help for the current situation but it appears if you had purchased the song on your home computer that you sync with you could have easily moved it to your work computer. As you've seen the inverse is not so easy.
http://support.apple.com/kb/HT1727
Use your iPod and iTunes 8
With iTunes 8 you can transfer iTunes Store purchases that are synced with your iPod to any authorized computer. Let's say from your home to your work computer. Here are the steps to transfer purchases from your iPod.
- Make sure that you are using the latest version of iTunes 8 and iPod software.
- Authorize your computer by choosing Authorize Computer from the Store menu in iTunes.
- Attach your iPod to the computer that contains purchases.
- From the File menu, choose Transfer Purchases from iPod.