Recluse: I think part of the problem here is that everyone is using the term "WiFi" and "Internet" sort of interchangeably when they are not the same thing, which may be confusing you.
Since you are communicating with us on this forum, you clearly DO have Internet service -- so I'm not sure why you appear to be under the impression that you can't buy a wireless router (I strongly recommend the Airport Express or Airport Extreme, given your need for reliability) and set up a Wi-Fi network in your home, hopefully that is just a misunderstanding on your part.
The Bluetooth idea will MOST DEFINITELY not work so let's just forget that entirely.
As stated by others, a Wi-Fi router will let you create a network in your home. It is not repeat NOT dependent on an Internet connection, though of course it appears you could have that if you set up a Wi-Fi network. In either case, the iPad and the printer would then communicate. They just need to be on the same "local network," not necessarily the Internet.
Obviously, once you've connected the Wi-Fi router to your existing modem, you will also enjoy your Internet connection on the iPad as well if you choose to do that.