Provided that you mean Hash first (BCrypt) and then encrypt the hash, security should not be weakened, yet you are not improving security either.
Encryption is, by definition, a reversible scheme. Since there really is no use-case for which you would require the decryption in this case, encryption is the wrong tool for the job.

If you are looking use a 'secret key' in combination with password hashing, your should make use of an HMAC instead (commonly refered to as 'using salt &amp; pepper'). For more information on HMAC and Hash see: Password Hashing add salt + pepper or is salt enough?. For a discussion on how to implement this, see: How to apply a pepper correctly to bcrypt?.

Are there any disadvantages to encrypting the password hash?
I have a hard drive that gets plugged into several machines. One MacBook Pro running Mac OS X, some Ubuntu and Fedora Installations and sometimes Windows XP or Vista. Therefore, I formatted it NTFS to be able to read and write on it no matter which machine is used. On Mac OS I installed MacFUSE to do this. 

The Problem is, when the USB device is removed from a Windows box, without using the "remove hardware" function from the task bar, the drive is locked. When I wnat to mount it in Mac OS, I get an error message and have to connect it to back to Windows and cleanly unmount it.

So, my question is: Is there an easy way to use the drive on every computer / OS without mounting problems? 
