I posed the very same Bashi-Bazouk question a few years ago,
and members of the LAF were very helpful.
They contributed many images of Bashi-Bazouks, in a wild array of wardrobe.
However, as has already been mentioned in this very thread, Sudan Campaign Bashi-Bazouks were no longer 'real' BB's, but as sort of Egyptian, home grown, frighten the peasants sort of force. "Go Strong Into The Desert" explains this at some length, AND in the text mentions that by this point Bashi-Bazouks were wearing a sort of Zouave-ish uniform issued by the state. The book also includes some very helpful water colors of BB's and these seem to indicate that the semi-official uniform was 'mostly white' with red or blue trim. A less frequent alternative being 'mostly white,' with a blue jacket, and red trim.
My Bashi-Bazouks remain in their original paint scheme, matching the 1820-1850 oil paintings provided by members of the LAF. They look very nice, and I can't quite bring myself to re-paint them in more historical hues.