Sounds like you have Original/traditional Medicare and a Medigap plan to cover the 20% Medicare does not pay. Me too, I have Original Medicare (Parts A and B) and I am so glad I do. I have had two surgeries, a stent and many PET and CT scans in the last two years and I have never seen a bill. And I had no problem self-referring myself to Mayo Clinic.
We have been discussing Original Medicare vs. Medicare Advantage plans in another thread on Connect, warning people about shortcomings of Medicare Advantage. It may sound cheaper, but if you have health issues you easily arrive at Medicare Advantage max out of pocket expense. My Medigap plan costs me much less than I would be paying with Advantage now and I go to whatever doctor I choose when I choose.