As mentioned by ee-ea, you would include the whole amount of income reported on the 1099 as business income and then claim the miles driven as a deduction to offset that portion of income.
While working on your Schedule C, look for the Business Vehicle Expense section to enter the details of the vehicle you drove for business purposes. You will need the total number of miles driven for the year as well as the number of business miles you drove. You will have a choice of claiming the standard mileage deduction or actual expenses. Keep in mind that if this is the first year you have used your vehicle for business purposes, then choosing to use the standard mileage deduction will allow you to switch to the actual expense method in future years if it is more beneficial.
After you have entered your business miles, then the income from the reimbursement should be wiped out by the deduction unless you were reimbursed at a rate higher than the IRS standard mileage rate (which would be unusual).
Take a look at the following TurboTax article to learn more about claiming vehicle expenses:
Business Use of Vehicles
@Susanlph
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