Can you use the controller in your bathroom? Several factors will contribute.
http://www.nintendoworldreport.com/news/32157
The Wii U GamePad "will be fine within the same space" according to Toru Yamashita of Nintendo's product development department during the latest Iwata Asks.
Some individuals will be able to use the Wii U GamePad at a further range than others, but it will all come down to the interference between the console and the controller.
Iwata explained that "Differences will arise depending on whether you live in a house made of wood or an apartment of reinforced concrete, and what materials the walls are made out of."
Nintendo Engineering Manager Tat Iwamoto further explained "If you place the Wii U console in something like a metal TV stand it may deflect the radio waves thus reducing its usable range. Radio waves weakens by the square of the distance, so even within the same space, too much distance could make them weaker, and having obstacles in between would be a disadvantage."
Ultimately each households range will be different. Wii U owners will have to experiment on their own to find the maximum range they can still use the GamePad. Last month Nintendo commented that the Wii U Gamepad works best within 24 feet of the system. This distance is most likely a rough estimate.