Fastest & easiest way would be a cab.
If you want to take Disney transportation, you could take the monorail to the MK and then the bus directly back to the BWV.
If the studios were still open, you could take the bus there and then either boat or walk back to the BWV. (You could also monorail to EPCOT, but that involves a change of monorails at the TTC and a pretty long walk (20-30 minutes at an average pace) from the main entrance of EPCOT, thru the park, and out the International Gateway to the BWV.
Another option is to take a bus to Downtown Disney and then transfer to the BWV bus. I would pay the $15-$20 for a cab rather than do this because you can wait a long time for a bus back to the resort at DD. Of course, if you want to shop or enjoy DD/PI entertainment for awhile first, then it's a viable option.