Hi!
I'm currently writing a music composition that will be based on a fictious bedouin tribe's culture (and additional lore but that is beside the point). Speculative art :) !
I've found plenty of information on politics, social structures throughout the ages and so forth, but it is difficult to get detailed information on old bedouin music (from before early modern times, that is). Generally, ancient music is a difficult subject, but I at least know where to look when it comes to european music.
I'm most thankful for any possible sources on the subject, general bedouin art history is helpful too!
/Mortimer
Have you tried /r/ethnomusicology? There might be somebody over there at least a little closer to that. I don't know if there's any people into Bedouin music here at AH...
Some of the stuff I can think of that might help (not exactly what you asked for, and I guess you might have already looked at these):
Amnon Shiloah - Music in the world of Islam. Some of the Pre-Islamic topics might help.
Are you familiar with Arab music and its theory? If not, I guess a look at these could be better than nothing.
Al-Farabi's al-Musiqa al-Kabir (Book of Great Music).
Let's hope there's somebody here into this rather specific stuff.