how do i label my images in bridge when the images are stored on an external hard drive?
If this are normal images (jpeg,PSD etc.) just point Bridge to the folder you want (use the folder panel for easy navigation or type in the path in the path bar by clicking double on the current path showing.
Wait for bridge to build the cache and make your selection with either labels or rating or a combination of both. All changes will be written in the file itself and therefor read the next time you have them in the content panel.
If the files are Raw files from the camera you have to check the Camera Raw preferences general section to ensure you have set "save image settings in: to 'Sidecar XMP files'. The label and rate info are written to those XMP files that have the same filename but extension '.xmp'. This are by default hidden files and as long as you use bridge to move the files around those files are traveling along. Otherwise when doing manual be sure to include those files.
Raw files converted to DNG don't have such sidecar file because like normal image formats the info is written into the DNG file itself.