Simple Cloth simulation seems to work quite well with Wind effector.  
I know you asked for bone anim.

[![enter image description here][1]][1]  
Just play anim and move (G) the Empty arround.

It can be used as a proxy mesh for more detailed model with Surface Deform Modifier.

[<img src="https://blend-exchange.giantcowfilms.com/embedImage.png?bid=RMsoPE1z" />](https://blend-exchange.giantcowfilms.com/b/RMsoPE1z/)


  [1]: https://i.sstatic.net/5iHYa.gif