If you are using NHR and Elements (at least I have seen this on version 6 and 8) then Adobe Bridge will not launch. This is because the /Users/~/Library/Application Support/Adobe folder is redirected to tmp because Adobe Reader 9 doesn't work with Network Homes. Adobe Reader just won't launch, so that Adobe folder needs to be redirected. However, if the Adobe folder is redirected then Adobe Bridge doesn't work.
Solution: I don't really have one, in my environment only mobile users (with an account on the local workstation that syncs to the server) uses Adobe Photoshop Elements, so I don't redirect the ~/Library/Application Support/Adobe folder. But, at least you will know where to look for the problem with Adobe Bridge.
This was verified with client OS 10.5.7, 10.5.8, 10.6.1 and 10.6.2. Also with Adobe Photoshop Elements 6 and 8 for the mac.