The short answer is...yes. Mutant hand shapes are required.
The long answer is... you have to be a little imaginative in your fingering. eg: in the first bar finger: 2-1-3-4-2-3-4-3 (1 is index).
Don't be afraid to change the tabs if you can find a way to play it more comfortably a different way.
JS Bach didn't sit down and write this out in bass tab

.
Example: Check out the 3rd bar:
---------10----10---------10----10-|
-------12----12---------12----12---|
-----10----10---------10----10-----|
-7-10-------------7-10-------------|
You would probably finger the 2nd and 3rd notes (D+G) as a barre with the 3rd finger then move the hand up to catch the D on the 12th fret.
I prefer this:
-------7-10--7-10-------7-10---7-10-|
---------------------------------------|
-----10----10---------10----10-----|
-7-10-------------7-10--------------|
..playing the high D's in the 3rd bar on the G string keeping it all in the one position and making it FAR easier to get back to the root note on the B.
Nice piece.