I essentially run the business, but I do not own it and I got paid nonemployee compensation from the owner/my boss.
You aren't an independent contractor if you're an employee.
If you received Form 1099-NEC you were considered an independent contractor. The IRS requires independent contractors to report their income on a Schedule C, Profit or Loss From Business. As an independent contractor, you pay 100% of your self-employment (SE) taxes. On the plus side, you can deduct your mileage and any other expenses you had in relation to this job.
TurboTax is not asking you about your bosses business, it's asking about your business.
To enter your self-employed form 1099-NEC:
To enter your self-employment business expenses, like home office, vehicle mileage, and supplies, click here.
For additional information, please see Am I an employee or an independent contractor?