College of Alameda's academic senate bank account does use our district's TIN ... but I have to say I think what we do now is something grandfathered that might not be approved if we are doing it as something new today. (Also, the kind of senate due deduction we receive from the district is pretty small---like less than $200 per month---so I think they are willing to let us get by, even if we are not doing everything by-the-book.)
I did think briefly about getting a proper IRS tax-exempt status for our college academic senate ... but that seemed like too much trouble for too little benefit (basically ability to receive tax-deductible donations; we run charitable things through our district's foundation, which runs scholarships, etc.).
BTW, Peralta District's academic senate does not have its own bank account; we do have a budget line in our district's budget, and everything we do---like paying for ASCCC event attendance costs---runs through our district's normal process. I think this is the normal procedure/process (... although I'm not sure how that will work with voluntary due deductions; our district academic senate doesn't collect due deductions from faculty).