Upvote:1
If your country is in the visa-exempt 90/180 list for Schengen, then you are indeed exempt from needing a visa for your first ninety days in Schengen. Your time in Bulgaria does not affect it.
When your ninety days are over, however, your visa (if in effect) means you are not guilty of overstay.
Upvote:2
No.
You have a visa to enter the Schengen area and you are allowed to enter Bulgaria as a visitor. That Bulgaria is an EU country does not mean you violate your Schengen visa at a later time for a different purpose. The only problem you can get is if you stay longer in Bulgaria than visitors are normally allowed, or if you violate some other condition of your Schengen visa. But if you're a visa free national for Schengen as well, you could even enter the Schengen area earlier than your D visa starts, as a visitor, and start your D visa stay without entering "on" the visa.