Photoshop and other members of the Adobe software family create various temporary files in the user directories. Which of these files can be safely omitted from backups? So far, I have not found a list on adobe.com.
Generally, any temporary files created by Adobe software exist only when the program is running and a document/file is open. Once the document is closed the files disappear, as they are only temporary.
Exactly where in the Users Directory are you seeing the files that you are referring to? What is their suffix? Are you using Photoshop Elements, or the full version of Photoshop? If you are using the full version, you can set Scratch Disk (if you have more that one disk) for both Photoshop and Illustrator. InDesign and some other programs don't have that option, and a temporary file will appear in the same folder/location that the actual open file is stored in. And, will disappear when the original file is closed.
I wish that I could be more helpful. I have Adobe Bridge CS3, but have not purchased any items from the Bridge Store (which I assume are photos). The only help that I can potentially provide are the minimal Google searches (links following) that I keyed in with your concern. You will probably have more of an idea of how they apply to your particular situation. Because of my limited exposure to your situation, I'd prefer not supplying any concrete answers or opinions. I hope it helps a little.
What it comes down to is that these files could safely omitted from backups with no loss of real data.
My backup media may last longer after I change the scripts to omit the cache files or configure Bridge to use another location for caches which is not included in the backup. This applies to both Time Machine and Retrospect backups. It really makes no difference to clone backups like SuperDuper or CCC, except for backup run time.