When I input them as miles driven for business, it brings my net income well below zero.
Yes to offset your income, you may report any related business expenses. In the case of car-sharing, Vehicle Mileage is probably your largest expense. You can either take the standard mileage deduction (54 cents per mile for 2018) or your actual expenses. Substantial record-keeping is required to deduct vehicle expenses. TurboTax will walk you through these options and help you choose which is best for your situation.
As the owner renting your vehicle, you are considered self-employed and must report your business on Schedule C
The link below has information that you may find useful.