Perhaps Amulya could explain it better though.
I heard of Tribaret within a few months of starting classes and was interested by it myself but I am not sure if it is just a passing fad or an lasting rebellion against the industry standard costumes of Tribal/Fusion/Cabaret dancing (Tribal isn't pretty enough, Fusion is too dark, and Cabaret is too polished/flashy). )
Long before Ansuya came on the scene there was this fusion of mixing kuchi jewellery and cab gear mixed in with beaded belts and sequinned bras all topped off with Ghawazee and Bedouin headgear. It was just something we did coz we couldn't afford a real expensive professional costume and it also looked more interesting visually. It was all way before we'd even heard of or been exposed to anything from the States or even FatChance and certainly not BDSS. A friend of mine went to Turkey and brought all this Afghan jewellery back and we made up stuff from it to complement the cheaper looking cab gear we had. We called it Gypsy style, coz that's what it looked like and we'd wear choli tops to match with little pill box hats. It all seemed magical back then... before it became a perceived faux pas to do such things and call it bellydance. I'm getting to the stage where I feel more and annoyed that people are pigeonholing this dance into compartments of their own making and then getting uppity if someone dares to deviate from their considered 'norms'.
Tribaret is not a style of dance, as far as I can see, but a fusion of costuming. The footage I've seen of Ansuya, she does bellydance, and the only remotely 'tribally' feel she offers is the use of zagat.