I was working at a hospital and I passed out and they took me to the ER and ran tests?

If the tests were required as a result of an accident at work you will be covered under Worker's Comp.

If not, the hospital will file against your insurance company. If you carry no insurance, they will bill you. As an employee you should ask that they give you a hefty discount if they bill.

Unless they have some 'free medical for employees' policy at the hospital, you should pay for it. Employers are not liable for their employees' health. And it wasn't an 'accident', it was you passing out.

Presumably you have medical insurance since you have a job, so you should submit the bills to the insurance company.

Doesn't sound like it was work-related, unless something fell on your head or something. You, or your insurance, are responsible for payment.