Cork has been used for mounting orchids and bromeliads for years. Tillandsia airplants grow best when attached to cork bark. The uneven surface is perfect for finding just the right spot to attach them to. They will quickly root and become permanent. ​
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I just returned from tens days in Portugal and spent several days in Alentejo, walking in some old cork oak forests. ​Alentejo is in south central Portugal and is where the majority of the cork trees are farmed. 

Tree gardening is an easy way to create a micro climate for your tillandsia collection.  If you live in a zone that will allow you to grow your tillandsias outside all year, then this may be for you.  This tree garden was created in Goleta, California by Ted Umbour.  He attached each tillandsia to a piece of cork bark and then secured the cork to the Jacaranda tree.  Cork makes a perfect host for most all tillandsias.  Cork is not prone to fungus and retains just enough moisture to encourage root growth.  No need to use any moss with the mounting, as that would keep the base of the plant too wet.  

The tillandsias are secured to the cork with a double strand of 20 gauge coated steel wire.  The wire is wrapped around the base of the plant and then twisted together on the back of the cork.  You will need to drill two holes in the cork to get the wire to the other side.  Twist and tighten the wire so the plant is held firmly.  Be careful that you do not damage the plant when tightening the wire.  Once attached to the tree the tillandsias are easy to water with a hose.  All the moisture that the tillandsia receive will add to the humidity in tree canopy.  The added benefit is that the plants will get plenty of dappled light and air movement, just as they would in their natural habitat.  Your tree garden will do better with more plants than with fewer.