It depends on the passport that your wife is carrying. Except that as a spouse of EU citizen, she can ask from Bulgaria a special residence card and travel as a European citizen.
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Can my spouse travel to Greece and Europe with me?
I am trying to find out the current travel restrictions in Greece. I am a Bulgarian citizen and my husband and children are Americans. We are currently in Bulgaria. Can my family travel with me to Greece and other EU countries?
Answers
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If a non-EU citizen is married to an EU citizen, he/ she can live with his/her spouse in the EU country in which he/she resides. If you are staying in your host country for more than 3 months, you must apply for a residence card and declare your presence to the competent authorities You must apply for a residence card at the beginning of the host country within the EU, usually at the town hall or local police station, within 3 months of your arrival. If your family members, had already the above residence card for family reunification reasons with you as a European citizen, they can travel freely to Greece or any EU country. By the way, Bulgaria was among the first countries from June 15 for which Greece opened borders.
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From July 1, 2020, all international flights to Greece are permitted, except flights from nine countries, in which the USA is included. However, due to the fact that you are currently living in Bulgaria and all of you will travel from Bulgaria to Greece, there is not any travel restriction.