Hi and welcome,
Possibly try this, open your AirPort Utility and click on Manual Setup and select Disks. Go to the File Sharing tab and make sure Enable file sharing is checked. I would also recommend securing your shared disk with a password or some kind.
Hit Update and wait for your Base Station to restart.
In a Finder window connect to the AirDisk under the Shared items in the sidebar. You may have to login by clicking on Connect As... and entering your password, that may not be obvious but it is an important step.
Now open the Time Machine preferences in system preferences and make sure it is on and then select Change Disk and click on the AirDisk. It will start preparing the disk this may take sometime to do the first backup,
You just need to make sure that the AirDisk is mounted.
