EU/EEA investors can carry out insurance activities in Bulgaria wuithout restrictions. Non-EU/EEA investors may carry out insurance activities in Bulgaria following the establishment of a branch, subject to reciprocity requirement.
"Section II - Carrying out an activity in the Republic of Bulgaria by a third-country insurer
Conditions for conducting business
Art. 56. (1) An insurer from a third country shall have the right to carry out insurance activity in the territory of the Republic of Bulgaria through a branch registered under the Commercial Act, after obtaining a license from the Commission under the terms and procedure of this Code and its implementing acts. The license may cover insurance business only by classes of insurance for which the insurer has been authorized to carry out insurance business in the country of its registered office. Simultaneous activities under Section I and Section II of Annex 1 through a branch shall not be permitted.
[...]
Refusal to grant a license
Art. 58. [...] (2) The Commission may refuse to grant a license even when it finds that the competent authority in the country of the insurer's domicile does not apply the principle of reciprocity in providing access to the relevant foreign insurance market to Bulgarian insurers, and where the third-country insurer poses a risk for the national security of the Republic of Bulgaria. [...]" (Decree No. 282 on the Insurance Code of  the Republic of Bulgaria, 29 December 2015 [google translated])
Decree No. 282 on the Insurance Code of  the Republic of Bulgaria, 29 December 2015 [google translated]
[<a href="https://dv.parliament.bg/DVWeb/showMaterialDV.jsp?idMat=99637">Code</a>]