Is it possible that the user in question has a Jaz or Zip drive or other type of drive that is already taking H: ?

Try the code again, but this time use P: instead.

USE P: /DELETE
USE P: @HOMESHR

Also try doing the same from a DOS prompt on the machine.

NET USE P: /DELETE
NET USE P: \\SERVER\BSMITH$

If this does not work from a DOS prompt it is not going to work from KiXtart either.

If it does not work from the command prompt, then what Microsoft Error does it give back?

Are you sure the BSMITH account has Rights on the BSMITH$ share?
Does the user have NTFS rights on this folder?