I think you're confusing terms here. Bedouin is an Arabic word that refers to Arab nomadic/semi-nomadic/formerly-nomadic tribes, with the word etymologically linked to the desert. Something like "Berber Bedouin" would be a contradiction in terms.

As for the Bronze Age, the best early history of the Arabs that I know of is Robert Hoyland's "Arabia and the Arabs: From the Bronze Age to the Coming of Islam." Even that only deals very briefly with the bronze age, as the best information we have about Arabia in this period is that, basically, it was a center of trade, and that's about it.

The Bronze age also ended about 2000 years before the Arab conquests.

So basically I'm just not really sure I understand your question. Do you mean what the ethnicity and language nomadic peoples in the Middle East would have been? And when? Also where, specifically? The Middle East can be defined as everything from the Atlas Mountains to the Oxus, which in ancient times would have contained innumerable ethnic groups, tribes, and languages.