@RalphNord
I've not heard of the "address registration" issue, and I've not personally done such a thing. Rather, my experience is that my Notary Act or rental contract was required to do my residence permit... and they included this address on the new card. My card has been accepted as proof of ID and proof of address when I've visited banks or utilities. There is no mention of this requirement/document in the D visa guidance, but I suppose it might be an issue for your subsequent residence permit.
There are a number of excellent immigration attorneys who have helped many of the members here. If you need names, just send me a private message. However, the guidance online is quite detailed, so it's perfectly plausible that you can do it yourself and gather everything needed for your D visa application at your local Bulgarian Embassy. Once you have your D visa approved, you fly back to Bulgaria, and then you do the final step to get your biometric residence permit. (Ballpark attorney fees 500 euros to help you with D visa application, and 1,000 euros to get your residence permit after your D visa issued.)
A rental contract is necessary (as proof of address in Bulgaria). It would typically be done in Bulgarian and English for a foreigner. You should note that the D visa application normally also requires the "landlord declaration" also (a separate document). At least one of the two documents must be notarized. Some immigration attorneys can arrange a rental contract (and the declaration) suitable for immigration purposes (but not for living in). Might be around 500 euros, I'd guess, and leaves you free to figure out where you really want to live after you complete the residence process.
If you want a real place, I recommend BulgarianProperties as they have plenty of rental listings all over Bulgaria. They have a lot of international clients, and they can cope with remote transactions.
The Health Insurance for Foreigners is easy peasy. It takes about 10 minutes in any insurance broker, and costs around 100 euros. You don't need a translator or notary, the policy is issued in Bulgarian.
Some bank branches are tricky now, they want to see your residence permit (which you don't have yet). So don't be discouraged if you need to visit several banks/branches before one says yes. Your rental contract will help a lot. As will proof of your income/pension.
Once you get an account, the best proof is to get the bank to print a statement (after you've paid in a chunk of cash, ideally). Your bank should put an official stamp on your statement. This is a proof that you have an account (and that it has money in it). It does not need a translator or notary either.
Financial means usually not an issue for Americans. The official minimum wage here is about 400 euros per month. D visa issued for 6 months, so that's 2,400 euros.
Good luck with your trip!