I am writing this aswer because many have a misunderstanding of how the US healthcare system works.
The test is free, as discussed by JRE's top answer. Access to the test is in the $100 range.
Rossi did not understand how the US medical system works
Which is to say, the person used the US medical system very inefficiently.
The US does not have single-payer state-provided healthcare. Americans either fall under a government insurance program like VA or Medicare, or private insurance like Blue Cross, or go uninsured.
For insurance programs, only certain doctors and hospitals are "in-network" meaning they have agreed on payment rates. Someone on a private or government plan chooses an in-network doctor to be their primary care physician, if they refuse to choose, one is assigned, but this can be overridden.
There are also urgent care centers everywhere, about half as common as McDonald's restaurants. They provide similar services to PCPs but with longer hours. They serve both insured patients after-hours, and act as PCPs for the uninsured. Their visit fees are $75-150 depending on market. Not great, not bad though.
So for insured people, there is a triage: the PCP for things which can wait until a possible appointment, then in-network urgent care, then an in-network ER, then an out-of-network ER. Plans will cover out-of-network care in some cases including ER services. Plans have a 24x7 advice-nurse line to help you triage.
Uninsured people who are able to pay their bill, can use a similar priority: first to any PCP they have a relationship with on a cash basis, then to an urgent care, then to an ER. That is most cost-efficient.
Uninsured people who cannot pay have the simplest triage (the ER), but it is a sad story (for accountants); we'll get to that.
So the person should have gone to PCP or an Urgent Care center and gotten evaluated by a doctor. The doctor would examine (through interview) travel history, past contacts, and other risk factors, reported and apparent symptoms, and then determine which tests are medically indicated. since the doctor's goal is not to screen for Coronavirus, but to heal the patient. That is exactly what was done at the ER; they screened for several things and found a simpler disease (flu) that explained the symptoms; as a result did not do a Coronavirus test. The doctor is thus a gatekeeper to the testing system. The test may be free, but the doctor must be paid.
Gatekeeping is even more important given the shortage of test kits.
ER prices really are that crazy
There is a special rule for ERs: they cannot turn away a patient in urgent need. That means they are a magnet for the uninsured. PCPs or Urgent Care will stop them at the receptionist. So the uninsured just go straight to the ER for everything, even though it is an inefficient (high real cost) way to provide most types of care.
This is a fiscal problem for the hospital. For the insured, insurance only pays very low, negotiated and competitive rates for ER services (say: $300 for the actual ER visit), which approximate the real cost of providing the service in an ER setting. There's no margin there. The best place to recover losses to the uninsured is from the minority of cash patients who do pay.
On the other hand, in many foreign countries, the belief among their wealthy is that the US has the best care in the world. So the system, particularly hospitals, gets a lot of cash business from foreigners.
This has created a perfect storm for obscene retail prices for ER services, that do not reflect the genuine cost for providing the services. Since the indigent won't pay, retail prices are tuned to get the most from the wealthy who will pay. Although it is true that getting non-emergent care in an ER is much more expensive than at a PCP or Urgent Care, it is nowhere near the $3000 reflected in that retail hospital bill. This indeed is an artifact of how America does business in the medical business.
When insurance is billed, they are billed at the obscene retail rate, as claimed. Not mentioned is that the insurer goes "sh'yeah right, see our contract", or if out-of-network, the insurer haggles it down to something vaguely resembling contract rates (mind you, this happens every day; they all know each other, and it's old-hat for everyone).
That US ER's charge $3000 for a walk-up that involves a blood test: True.
By the way, someone confronted with such a bill should haggle ruthlessly and unrepentantly to cut that bill to a fraction.
The person chose the least efficient method for care
Perhaps not knowing the system (never having dealt with health issues before), the person went to a hospital. 90% of hospital business is complex specialist care which flows from a referral from a PCP, e.g. For an MRI scan or to see a podiatrist. But all that business walks in the side door during business hours, not in the ER (the ER has instant access to it, that being an advantage). Perhaps the person expected that the hospital would have a walk-up clinic service comparable to a PCP or Urgent Care that would efficiently triage: determine the most effective/efficient path to care. Nope: the only option they have for walk-up triage is the ER, which is equipped for anything (and you pay for that).
The person could have had the test done for no more than the cost of a doctor's visit and blood draw at a normal PCP or Urgent Care.