mdfind and the apostrophe
You need to escape the single apostrophe with a single backslash and do not quote the show name if it has an apostrophe, just escape any spaces with a single backslash too, as in the examples below:

$ mdfind -onlyin ~/Desktop/"Shows I Watch" Bob\'s\ Burgers
/Users/name/Desktop/Shows I Watch/Bob's Burgers
$ mdfind -onlyin ~/Desktop/Shows\ I\ Watch Bob\'s\ Burgers
/Users/name/Desktop/Shows I Watch/Bob's Burgers
$ 


It should actually work with the show name in quotes as in the first example you have under "Here's a list of everything I've tried:", it worked on my system.

$ mdfind -onlyin ~/"Desktop/Shows I Watch" "Bob\'s Burgers"
/Users/name/Desktop/Shows I Watch/Bob's Burgers
$