I've only seen one post here so far from someone who got it to successfully work far enough to reach a bathroom. It seems the range is shorter than even the standard Wii Remotes.
That would make sense, as the Wii remote doesn't have to work in such a short, bi-directional window of time, and it has far less data to coherently transfer.
I've seen a bunch of posts around here about people using the GamePad successfully in other rooms and even other floors.
Wii U Gamepad: User Feedback & Distance Limitations
"Works in just about every room of my house"
"I can play fine in the bathroom, my bedroom, and the bathroom in my bedroom (2 walls/doors and 30-35 feet)"
"Mine worked decently once I stopped moving in my room. I live in a 2 story apartment and my room is downstairs, probably like 40 feet away, diagonally through walls."
"It works in my Bedroom and there is another bedroom between my bedroom and the living room."
"I have access to it within the key areas of my house"
"Wii U is in my living room... Pretty close to the center of the downstairs. I can go all over the downstairs just fine except my kitchen where it needs to go through a couple of walls because of a weird layout. Upstairs is 100% fine too in both bedrooms…"
While most of the above don't explicitly mention bathrooms, it's implicitly suggested that they're getting far enough that a bathroom would be included in the range. Mind you, I cherry picked, but there's definitely a multitude of GAFfers who can do bathroom gaming.
I'm nearly regretting getting one at this point, that might change once I get my hands on it (still shipping) but if it doesn't I know I'll be glad I have one the second they show off a 3D Mario, Metroid, Zelda, basically any Nintendo developed game that isn't 2D Mario or Pikmin.
You're in luck, Nintendo released such a game at launch!