do the Bulgarians' accept new crisp 1's and 5's or Euro's?

Why would you want someone to set their own arbitrary exchange rate that won't be favorable to you? That's why they're happy to accept it. If they're happy, that means you're on the losing end (plus they won't give you change in EU or USD). In every country I visit, I get a minimum of local currency as I need it from the ATM (as opposed to large amounts I can't spend). Even if you lose a few Bulgarian levs, it will be an inexpensive loss. They also accept credit cards in the places you're likely to be visiting.

I would guess that they are unlikely to accept USD, except at a very poor rate, but since they are tied to the EU, you likely will find places that dual price in Lev and Euros, though again, the Euro price may round to something higher than the equivalent Lev.

Other EU countries that I have been to, Croatia for example, some hotels and other services are priced in Euros, solely for the convenience of tourists from Euro Zone countries, and cash is expected.

Our only visit to Bulgaria was 14 years ago, so maybe things have changed a lot, from when we got Leva from ATM's and used only that.

On our trip to Morocco 2 months ago though, only a couple of "places" (Riads) accepted credit cards, and our desert trekking company accepted cash in dollars, euros, or dirhams, but with pretty much everybody else, it was strictly local dirhams.

You mention crisp bills . . . the trekking company charged a 5% surcharge for credit card payments, so we brought $1,900 in crisp, new $100 bills with us from the USA. Unfortunately, they didn't mention anything about the bills needing to be totally "clean" until we arrived at their booking office, and they said their bank wouldn't accept the 5 bills that had a speck of highlighter on them. Our credit union marks some of their bills to help speed up their counting, maybe every 5th or 10th bill, with a highlighter mark. It's not like someone drew a goatee on Ben Franklin, and a 6th bill had a tiny, stray, 1/4-inch-long mark that had seemingly been made by a black ink pen - something you'd have to really look hard to spot. They said they would present all the cash to their bank, but that when we returned from our trek for a final glass of mint tea, if the bank had rejected any of the bills, we'd have to replace them with equivalent cash, or use a credit card. Standard banking practices in the USA can render some otherwise perfectly negotiable currency to be unusable overseas. Ironically, some of our dirhams were in less-than-perfect shape, but no one questioned them!

The question I want to ask is why would you want a foreign country to accept US dollars on the first place? Are euros accepted in North Carolina?

While Morocco, Israel and even Turkey is more than happy to take payment in Euros, I've never been anywhere in Europe where they are happy to take dollars in cash. Currency Conversion at high rates yes. As others have said, how many places in America take Euros?

As a Bulgarian who lives in Bulgaria, I can say that it is illegal to use any other currency than Bulgarian lev (BGN). 10 years ago when I worked in a casino in Sofia, we were instructed by the manager to accept only leva (lev-> leva), euros, and US dollars (which apparently was illegal at that time and it still is) so there may be places where it is possible to pay with USD. Anyway, all prices are in BGN and I doubt it that more than a handful of businesses would accept USD. You can buy some BGN at a bank or at a kiosk called 'CHANGE', though the first option is much safer than the second one. Of course, you can always pay via credit/debit card. Most places accept such payments. You can also withdraw leva at an ATM.