What version of Bridge are you running? (Bridge menu > About Bridge) and what has been disappearing when you select Desktop?
CS6 Extended, I have an iMac. It works with my external drives, but not any of the thumbnails for the desktop. When I try to open the desktop, bridge just disappears. One time it prompted me to purge my cache, which I did that. Now it just wants to reopen or close, but no thumbnails to see.
Ok, let's see if it's corrupted Preferences. Here's how to reset Bridge.
When launching Bridge, Command-Option (Mac)/Control-Alt (Win) + Shift to choose “Reset Preferences”, Purge Entire Thumbnail Cache”, and/or Reset Standard Workspaces”
I did the option, command and checked all three boxes of the preferences. Still Bridge disappears as soon as I try to open the desktop
Ok. here is a full troubleshooting helpdoc. Troubleshoot errors, freezes | Adobe Bridge | Windows, Mac OS
Repair Permissions with Disk Utility as well.
If nothing works a clean uninstall/reinstall is all that is left.
I also wonder if you see this behavior in other user accounts on your Mac.