D Visa for USA Citizens

As far as I know, Bulgaria does not discriminate when evaluating visa applications.  You should have the same chance as anyone else, and if you meet the requirements you should be approved. 

I'm sure Bulgaria will love to have your money spent in its economy.

This document links to the two pieces of legislation that cover getting a D-visa... http://www.mfa.bg/uploads/files/VISA%20(TYPE%20D%20VISA)(1).pdf

Warning- the two documents are long and confusing. I found the Bulgarian embassy was great at responding to me when I emailed them about getting a visa for my parents and letting me know what visa they would be eligible for and what documentation they would need. i would definitely shoot them an email before your embassy appointment to make sure you have all of the appropriate paperwork, because I have read other stories of people's visas being significantly delayed because they did not have the right paperwork.

From what I read, if you want to enter on the basis of being a freelancer, you will likely need a work permit issued to you from the department of labor approving you to be a freelancer before you can get your visa. It was a PITA to register as a freelancer in Bulgaria, not sure the process outside of Bulgaria though. But they don't issue a visa just because you want to live here- you need a valid reason (work, a functioning company that employs Bulgarians, being a family member of a Bulgarian, being retired, or investing a large sum of money are the standard reasons), so I am guessing the freelancer work permit will be necessary.

Additionally:
Your apostillized FBI fingerprints (apostilization can take a month if you do it by mail, so do it well in advance).
Proof of means of subsistence... usually a certified statement from your bank stating your balance.
Proof of accommodation. Not sure what they want from freelancers. I just used my in-law's address.
Proof of insurance. But in most cases you can hold off on buying medical insurance and buy it when you land- it is MUCH cheaper. (Like, I was looking up insurance online and it was $500-$600 a year for expatriation insurance. If you buy it in Bulgaria, it is usually less than 200 BGN a year.

Good luck.