This is part of a larger question, the relationships of the tribes with _any_ authority, Christian or Muslim; this is a story that goes back before the birth of Islam and isn't particular to the Crusades-- indeed, it's still a major theme of politics in places like Iraq and Jordan.

The tribes tended to dominate in the less settled spaces, and the fertile areas of Palestine and the Levant were more densely settled, less subject to tribal authority, more to governments, whether Byzantine or Umayyad, Seljuq or Crusader.

Speaking very generally -- which is the only way one can, because we often have only the most general of traditions with respect to the Bedu and their interactions with authority during the Crusades-- the Bedouin inhabited places that the invaders neither could live in nor did they want. You can see the same pattern even today, with Israeli settlement-- for the most part, the Bedouin are the one prior population that the Israelis _didn't_ substantially displace, because for the most part they didn't live where the Israelis wanted to live (though note exceptions like disputes with the Negev Bedouin). Also note that the Bedouin have served and continue to serve in the Israeli Army

Kurt Franz characterizes the Bedouins' ambivalence with settlement and the political attachments of settlement this way:

These groups (exemplified in the partisans of the Zikrawayh-Ismailiyya, mostly from the Banü Kalb and the Banū Khafaja) kept to what I have called a primary type of Bedouin exercise of power: a mobile raiding economy based on an organisation conceived by the actors as tribal, leadership by shaykhs, dwelling in steppe habitats and continued pastoral mobility therein. These are ancient Bedouin behavioural patterns that were only slightly modified when the relevant group extended its outreach into tracts of cultivated land and interfered with the polity there. Slightly, I say, because opportunities to remodel power for the sake of territorialisation and institutionalisation were declined - despite the fact that representatives of the sedentary milieu sued for this. Even occasional innovations such as the acceptance of supratribal shaykhdom resulted ultimately in the reinforcement of original political potentials rather than in transformation. It was the choice of these groups to be permanently satisfied with rudimentary regimes. Moreover, some of the groups who did strive to adopt external forms of domination and develop state-like regimes (namely the Banū al-Jarrāh and the Banū al-Muntafiq) failed to do so, not least because deep-rooted patterns, such as short-sighted prédation, rash spending of prey, tribal egoism and shaky alliance loyalty, interfered with these aims

. . . and that strikes me as a very general description which has the great virtue of being true of Bedouin political interests across many centuries.

We do know that Bedouin had been in conflict with the Fatimids and Seljuqs prior to the Crusades, and that a dynasty (of sorts) had arisen from one of the tribes, the Banu al Jarrah, a dominant clan in the larger Tayy tribe confederation; often referred to as the "Jarrahids". We find Bedouin on all sides of the conflict, looking for allies of convenience as did the Bedouin in Wadi Musa, who around the year 1106 wrote to the Seljuq ruler Tuktakin in Damascus, seeking reinforcements for attacks against the Crusaders. As a reprisal, you get the celebrated story of Baldwin "smoking [the Bedouin] out of their caves"

Similarly Jarrihids were, very briefly (two years and some), the rulers of Jerusalem and environs, and in that period sought assistance/cooperation with the Crusaders, for example their leader Mufarridj gave orders to assist in the restoration of the Church of the Resurrection; but like any of their attachments, this was transactional and brief. The Encyclopedia of Islam's entry encapsulates the ambiguity and obscurity of their political relations

Finally, in 501/1107-8 we find a certain Abū ʿImrān Faḍl b. Rabīʿa b. Ḥāzim b. al-Ḏj̲arrāḥ coming from Bag̲h̲dād to enter the service of the Sald̲j̲ūḳid sultan. His equivocal behaviour in Syria —at times he was on the side of the Franks, at others on the side of the Egyptians—led the atābek Tug̲h̲tekīn of Damascus to expel him from Syria. In Bag̲h̲dād he offered to fight the Mazyadid from Ḥilla, Ṣadaḳa, and to bar the desert route to him. He went to Anbār and nothing more is heard of him.

That, it seems, is all that we know of This turbulent family who were not without significance as pawns on the chess-board of Syria in the 4th-5th/10th-11th centuries, whom the Fāṭimids alternately attacked and wooed, whom the Byzantines succeeded in using, but who seem to have created for themselves, in their own best interests, a rule of duplicity, treason and pillage.

The Tayy tribe are one of the constants of this story -- they still exist, though are typically referred to as the Shammar. They've always been "balancers" and negotiators, amenable to a deal with any party -- they were allies of the Byzantines for a period. You'll find good English language scholarship covering many of the tribes and their interactions with authority, nearly all of which follow the same line of compromise, opportunism and frequent renegotiation; there is much better information about more recent tribe vs state relations, for example Madawi al-Rasheed's Politics in an Arabian Oasis; while that's obviously _not_ the Crusader story you're looking for, after you see the same pattern of interactions many times, it becomes easier to infer how tribes might have regarded situations for which we don't have documentation.

The Crusaders' chroniclers do tell us a bit -- Albert of Aix [Aachen] comes to mind and the Gesta Francorum. All sources that I've seen characterize the Bedouin ambiguously; they are sometimes enemies to be feared, sometimes not; there is no constant beyond opportunism and a resistance to any submission to authority. So the Bedouin did what they always do when a new power shows up-- they found how they could work with them, keep them from interfering with their lives, raid them or cooperate with them as might seem profitable in the moment . . .

​

Sources

Land Disputes between the Negev Bedouin and Israel

Southern Jordan in the Fatimid and Seljuq Periods

THE SEIGNEURY OF BEIRUT IN THE TWELFTH CENTURY AND THE BRISEBARRE FAMILY OF BEIRUT-BLANCHEGARDE

The History of Shammar

Politics in an Arabian Oasis: The Rashidi Tribal Dynasty

Albert of Aachen's History of the Journey to Jerusalem

Gesta Francorum ["Deeds of the Franks"]

The Crusader States and their Neighbours: 1098-1291

THE BEDOUIN IN HISTORY OR BEDOUIN HISTORY?

Encyclopedia of Islam, 2nd Edition, entry "Djarrahids" (NB-- the Encyclopedia of Islam is a great resource if you have library access, otherwise paywalled. Just note that they use their own accurate but infrequently used Arabic transliterations, making searching difficult, hence "Djarrahids" not the more commonly rendered "Jarrahids")