From your description, it should be reported as Other Income.
If the school considered you an Independent Contractor, they should have used 1099-NEC in which case you would file as Self-Employed using Schedule C.
As a Self-Employed Taxpayer, you would be able to deduct your expenses.
You would also be subject to Self-Employment tax. (FICA)
You would need to take depreciation on your vehicle (either as depreciation or by using Standard Mileage which has a depreciation component) and then "Recapture" that depreciation as personal income when no longer using the vehicle for business.
Additionally, the IRS could point out that you had no intention of starting a business and disallow the expenses.
If you were an employee of the school, you might get the reimbursement tax-free (if reported under an accountable plan) but you are not a school employee.
You can report the income on the 1099-MISC as "Other Income" without the intent to "make money" in which case it will be taxed (Income Tax) but not subject to Self-Employment tax.
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