I think it's spawned from the old contraction of Burlesque Queen: Burly-Q.
I only ever say 'burly' to my partner... i.e. 'I need to grab my burly stuff' - he knows what I mean.
I think any word over one syllable long has a tendency to get contracted through use (though speak to a linguistics student for a full explaination)!
My boy and I started shortening 'pyjama bottoms' to How-Trow (House-Trousers).
...It's just dawned on me that I'm a big loser!
So, rather than talk about what we DON'T like... what DO we like? I don't mind being referred to as a fellow burlesquer, but wouldn't like to be called that by someone from outside the circuit. I prefer Burlesque Performer, or Artiste.