Badger has two types of hoses, a vinyl hose and a braided hose. The vinyl hose has 1/8" threads on both ends. The braided hose has 1/8" threads on one end to fit the airbrush and 1/4" NPT threads on the other end to fit a standard compressor coupling.
If you have the vinyl hose, the part you need is Badger part no. 50-023 and you can see a picture of it here: http://www.badgerairbrush.com/access2.htm (it's about halfway down the page). I have seen them at some hobby stores, and Dixie Art (www.dixieart.com) carries them as well.
If you have the braided hose you should not need an adapter.