"what does it mean that the Bulgarian government now has more information about me than my own government?"

Nothing, really. You can always leave. That's what I tell myself living in the US. If I didn't want the US government to have my fingerprints, I could just leave.  As it happens, I don't think it's that infringing on my freedoms, and in Bulgaria's case, if used well, fingerprints can help solve a lot of crimes, eventually, and with a lot of political goodwill.  Wishing, I know.

Look on the brighter side: the US government has wider worldwide reach and can do more with your (or my) fingerprints than the Bulgarian government can.  There aren't any James Borne stories, Bulgarian style, yet...