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I have Windows 7 x64 and a brand new USB external 2 TB hard drive. I formatted it and I confirm it's empty.

I enabled BitLocker, and two things happen:

• 
  

  It is about to take at least 10 hours or even days:

  
  
  

  

  
  


• 
  

  The disk was initially empty (1.81 TB free / 1.81 TB total), but just after enabling BitLocker, it's like the disk is immediately full (5.99 GB free out of 1.81 TB):

  
  
  

  

  
  

No files are present when I open F: though.

Why does BitLocker take hours on a brand new empty disk?

Note: I've found this screenshot for Windows 10 here. Is the option "Encrypt used disk space only" available in Windows 7 for removable devices ("BitLocker To Go")?

Is the option "Encrypt used disk space only" available in Windows 7?

Unfortunately no. This option was introduced with Windows 8, as announced in the Microsoft TechNet Tip of the Day post BitLocker 'Encrypt Used Disk Space Only':

Previously, BitLocker encryption has been an ‘all or nothing’. Either a volume was completely encrypted or it was not. Windows 8 brings us a new option, ‘Encrypt Used Disk Space Only’.

Why does BitLocker take hours on a brand new empty disk?

Because without the Encrypt Used Space Only option, BitLocker must encrypt the entire disk, i.e. both data and free space (technically it only wipes the free space). This is also why the volume has only 6 GB free space during the encryption process. Here's the Microsoft BitLocker Team's explanation of what's going on:

Q: I enabled BitLocker on my volume and – poof! – all my free space is
gone! What’s wrong? More importantly, how do I get it back?

Good news: nothing is wrong and the only thing that you have to do to
get it back is wait. Here’s a high level explanation (some intricate
technical details have been omitted for brevity).

In the IT world “delete” usually means “remove from plain view” rather
than “obliterate out of existence”. Unallocated disk space is prone to
contain interesting data: rotting skeletons of compensation
spreadsheets, “deleted” text files with passwords and credit card
numbers, discarded autosave copies of top secret presentations. Hence,
BitLocker cannot just ignore free space when the volume is being
encrypted.

On the other hand, encrypting (or, to be exact, “reading, encrypting,
and writing back”) free space is a real waste on a typical volume that
is usually less than twenty percent full. As a performance
optimization, BitLocker simply overwrites unallocated space with
noise, thereby avoiding redundant reads. As expected, wiping free
space is about two times faster than encrypting data, but it still
takes considerable time on large volumes.

Now, free space tends to be very fluid. Unallocated chunks of disk
space appear and disappear all over the place, all the time.
Determining whether a given sector needs to be encrypted or wiped at a
particular moment of time is a considerable technical challenge.
BitLocker solves this problem by creating a huge file that takes most
of the available disk space (leaving 6 GB for short-term system needs)
and wiping disk sectors that belong to the file. Everything else
(including ~6 GB of free space not occupied by the wipe file) is
encrypted. When encryption of the volume is paused or completed, the
wipe file is deleted and the amount of available free space reverts to
normal.

Additional solution:

• Use a friend's Windows 10 to format the drive + enable BitLocker with "Encrypt used disk space only" feature on. It will take only a few minutes.




• When you're back on Windows 7 Ultimate, you can still read/write the disk

And even better:

• When you're back on Windows 7 Pro, you can still read/write the disk!
  

The latter is very interesting because "BitLocker is unavailable for Windows 7 Professional and it cannot be downloaded and installed.". My test showed that creating a new BitLocker-encrypted disk is not possible with Windows 7 Pro, but using (read+write) on an already-BitLocker-enabled is possible with Windows 7 Pro!

Full disk encryption isn't only about hiding content of files; it's also about hiding their presence or lack. A properly encrypted disk should look like it's completely filled with random data unless you know the encryption key.

BitLocker was probably fully formatting the encrypted volume, i.e. filling it with zeros, to make sure every part of it looks like random data before decryption.

Since Windows 7 BitLocker will encrypt the whole disk, it has to read and write to the entire volume. This can take much longer on an external disk due to bandwidth limits on some interfaces like USB1/2. Also external storage devices (non-SSD) tend to be slower spinning disks to help with reliability since external storage is moved more often.