You want 'em back or something?

Seriously, there are three main ethnic groups that have commingled, more or less, to arrive at the current population. One, perhaps most numerous, could have come from Persia, The other two groups are Thracian (a varietal of Greek, I think) and Slav.
But they've been "Bulgarian" longer than my English/Scottish/Dutch/Alsatian French family have been American (since before the US was founded; most of us have been on the continent since before 1700).