You go to your doctor, you have a suspected tick bite with a bullseye pattern around it and a red streak running away. Your doctor is concerned about tick born illnesses and the red streak suspecting the start of sepsis. They need to determine asap if they can treat you with docycline or if you need IV antibiotics. They need to assess your blood for a CBC to determine immediate risk factors like sepsis. They also need to asses for pathogens like Lyme disease, alpha-gal syndrome or that other tick disease I can't remember. This will determine what antibiotics will be effective, and if eating red meat will make you anaphylaxic, and you need to see an allergist if you ever want to eat red meat again
There's a place in town that can do the CBC, the test for alpha-gal is only done by two labs in the country, nearest one is in south Carolina two states away. There's more, but not many more that test for the other two diseases, the closest one is almost the whole country away in salt lake city.
You have to know ASAP to determine your next course of action.
In your proposal, do you call south Carolina and then fly there? Do you do the same to salt lake city? You've still got to find and negotiate with someone local for a CBC. Salt lake city doesn't have the same balance billing law your home state does, you could pay more than your cash price there if they involve another provider.
What do you do? Gotta act fast, or you could wind up with life long neurologically symptoms or even die.
I had a tick bite that was irritated (but not a bullseye rash that I could see) - phoned GP practise, doctor phoned me back a couple of hours later and discussed the situation, ruled out blood tests because they said they were inconclusive at best and arranged for a 3 week course of antibiotics. My wife picked them sup from a pharmacy later that afternoon as she was in town anyway. No direct costs, no mention of money, insurance or anything at the doctors or the pharmacy...
Edit: Discussions of US healthcare all seem insanely complex to me - but it all seems to be about insurance and money - which are the last things I want to think about if I am ill or injured.
I doubt your doctors office can commit a cash price for the lab they sent you blood too.
And try doing that at a hospital and see where it gets you