There is a great deal of choice for private English-language kindergarten and preschool education in Sofia, as many new excellent daycare centres have opened in the last decade. Many of these are in the leafy suburbs at the foot of Vitosha mountain, far from the traffic fumes, with just a few options for those that live in the centre. 
There are also several German-language kindergartens and schools, as well as a French-language school affiliated to the French Embassy.

After that, English-language education for older children in Sofia becomes a more complicated choice and prices are high, especially where the IB curricular is followed.

Though there are some very good Bulgarian state schools, we would only recommend going down that route if your child knows enough Bulgarian to feel comfortable and you are planning on staying long-term. Other options are private Bulgarian schools, which often teach part of the curriculum in English or German and part in Bulgarian, though again your child would need to know enough Bulgarian to get through the Bulgarian lessons.