And the projects that I'm running have 32-bit plugins.  Some work.  Some, like the Modern Plugins, do not.

Some older plug-ins need the host to run as administrator. I have read suggestions to set Bitbridge to run as administrator along with XP compatibility mode.

That's actually a great piece of advice, and I have done so.  It seems that it's not making a real difference, because bitbridge.exe is not starting when Sonar X3 projects are loaded.  

I do not know why BitBidge is not starting when a project containing 32bit plug-in is loaded. Unless 32bit SONAR is loading the project. The Windows Task Manager should show the 32bit plug-ins in the Applications tab and BitBridge.exe in the Processes tab.The Windows event viewer may have logged the failure. This may require a call to tech support to resolve.

I have also had issues with some 32-bit plugins being invisible to X3, most notably TP Basslane and ValhallaFreqEcho. They all worked fine in X2 and at some point along the X3 cycle just stopped showing up. Definitely something wrong.

After speaking with Dean in Tech Support, it seems that the VSTs are not showing up as such in the registry.  I've tried cleaning up my C++ development libraries, to no effect.  So it seems that the answer via tech support is not successful.

I found success by going back to JBridge, renaming different versions of the same plugins, and then running those plugins through JBridge again.  I now got everything back up.
 
So I guess if you're having issues with Bitbridge, and you don't want to install the x86 version of Sonar, try JBridge.  It's not free, but the cost is rather minimal.