To get an Anytune exported song into Garageband for iPad you have a couple of options.
Apple does not allow developers to put content into the iPad music library directly. You could email yourself a copy of the exported song or use Open-In export to copy the song to an app such as Dropbox which will then sync the song file to your computer. On your computer you would open the email (or Dropbox), and drag the file into iTunes. You can then add that song to a playlist and sync it back to your device using the normal iPad music sync process.
From there, you should be able to use the GarageBand Sampler instrument to import from the Music app by selecting the Music tab.
With Audiobus, you can use Garageband to record Anytune as it is playing back. This is handy for getting smaller loops or samples for use with Garageband, but does require a copy of Audiobus. There is a video here that shows the process:
AudioShare is a utility app for managing music documents. You could export tracks from Anytune to AudioShare using Open-In. From there, you could make use of AudioShare’s Audio Copy/Paste support to Copy the the audio and then go into Garageband and paste it in.