I know this is kinda old, but this will hopefully clarify why this would happen...
It has to do with your local permissions versus your mapped drive permissions. If you are mapping a drive with either an Active Directory account, or an account on another windows machine on your network, and you use Bulk Rename with "Run As Administrator", you are actually telling the Bulk Rename executable to use an account that most likely doesn't have permissions to access the mapped drive's network location, even if it's a local administrative credential.
Just make sure the account you are logging into your computer with is a member of the Local Administrators group, make sure that account has permissions to read and write to the network location of your mapped drive, and run Bulk Rename without "Run As Administrator", and it will work great
