Actually, I start bellydancing when I hear lots of songs nowadays. Not in public, though, but if I do hear a song, i start imagining my choreo.
I do the same thing. I'll be sitting in a restaurant and some rock song will come on, and I'll think "Hmmm, I can picture a cane dance to this..."
I actually started dancing after hearing Corvus Corax, since they inspire me like no one else. I'm choreographing a couple fusion pieces to some of their music now (which is easy, because a lot of the rhythms they use correspond nicely to familiar bellydance rhythms). Currently I'm working on this one:
Corvus Corax - "Oro Se Vie". (It's a Balkan folk song performed in semi-accurate/semi-fantasy medieval European style.)
My first solo, this past December, was to
"Gulan Du" by Mari Boine. That's what the picture in my avatar is from.
I usually dance to various types of world music because it's my favorite genre. I always be sure to do my research when dancing to a particular culture's style of music, and join a forum or two for that culture to make sure I'm doing it in a respectful way. (They're usually very nice and sometimes a couple of them tell me that they're bellydancers themselves, or considering taking classes.)
I call my style "fusion." I use entirely bellydance moves because that's what I know (I've taken Egyptian, American Cabaret, Turkish Rom, ATS, and some others, so that's where I draw my moves from...that makes it also a fusion within bellydance styles); I just use what fits with the music. I also always interpret the music when I dance (I read a quote from someone, I forgot who now, that said a dancer should look like she's creating the music by dancing, and that's stuck with me). Usually the music I pick is Middle Eastern inspired, and my costumes are also heavily bellydance inspired, but I like to make sure people know that what I do isn't exactly bellydance.
I just dance to whatever music inspires me. If I understand the soul of the song, a choreography just starts naturally forming itself in my head. If I think it's a great idea and would be entertaining to watch, I perform it.
(I'm also a little paranoid to actually dance to Middle Eastern music in any official style, even though I love it, because I'm always afraid I don't know enough and I'll accidentally do something I'm not supposed to do for that style. Fusion lets me breathe easier.)
I hope this isn't terribly wrong of me.