Bridge does NOT use the same thumbnail cache as Lightroom. If you open Bridge and go to Edit > Preferences > Cache you'll see where the Bridge cache is located. By default it is created on your installation drive but you can relocate it anywhere you choose.
Lightroom previews; both thumbnails and large previews, are saved in the Lightroom 3 Catalog Previews.lrdata folder that is created in the same folder with the LRCAT catalog. Those previews are distinct from the thumbnails generated by Bridge.
What is shared is the Adobe Camera Raw cache and that is different from either the Bridge thumbnails cache or the Lightroom previews cache. The Camera Raw cache is constrained by the amount of disk space assigned and only generates a dat file when the actual raw data is viewed. That means when you're looking at thumbnails in either Bridge or Lightroom, dat files are not created. Its only when you open a file in the Lightroom's Develop module or in ACR (running under Bridge) that dat files are generated. And since the ACR cache is limited by the amount of assigned disk space, the older dat files drop out when you open newer files.
At the end of the day its your choice but you're restricting your system performance by putting your cache on a Drobo. If you're so concerned about the small possibility of losing previews there are many better solutions from basic apps like SyncToy to more advanced backup applications.