I have the same problem in Bridge CS6. I discovered a workaround that I don't believe has been mentioned yet (if it has, I missed it and ask your pardon): In Photoshop, select File>Open and navigate to the folder with the photo or photos you want to open; select one or more images; set Enable to All Readable Documents and Format to Camera Raw. If you wamt to open a jpeg or tiff file make sure you set Format after you've selected the image(s) or it will automatically select the original file format. I found this strategy works in Photoshop CS6 as well as in CS4.
This is, of course, a workabound rather than a solution. Like others, I've found that if I double-click a raw file in Bridge CS6 rather than trying to use the contextual menu, images open just fine in Adobe Camera Raw. However, this will not open Camera Raw without first launching Photoshop - if it's not already open. It won't enable Camera Raw in Bridge itself. So this is still a workaround rather than a solution for the root problem - which is not being able to use Adobe Camera Raw in Bridge as we should be able to do. Apparently not even Adobe has a solution, even for ligitimate license holders.