Edited above Whoops: forgot to explain. This is in reference to FMGo 11.
Thank you for your posts.
If you have Airport Extreme, I'm not sure why you want to bypass AirPort.
On your Mac, go into System Preferences, click Network, and select either Wi-Fi (Mac OS X 10.7.x) or Airport (Mac OS X 10.6.x and earlier). Check the settings for Wi-Fi. Then, go into your iOS device, tap Settings, tap Wi-Fi, and make sure you are on the same Wi-Fi network as the Mac.
Launch FileMaker Pro, and open the hosted file. Launch FileMaker Go, and enter the local IP Address of the Mac to see if the files can be seen.
If this still fails, then on the Mac, launch a browser and go to whatismyip.com. Verify the IP Address. Then, in FileMaker Go, use that IP address and see if you are able to see the hosted file.
Keep me updated with any progress.
You can get the address of the computer hosting the database under File:sharing... for both wifi and ethernet.