Does my Bulgarian company need an EORI number?

Only if goods cross the external border of the Union. The EORI number identifies the economic operator to customs; whoever is established in the customs territory of the Union registers with the customs authority of the member state of establishment, Article 9(1) of the Union Customs Code. It is assigned once and is valid across the Union; in Bulgaria the Customs Agency assigns it. For supplies and services within the Union nobody needs it. On the southern coast that means: a haul to Germany no, a haul through Malko Tarnovo into Turkey yes.