Hello I am Bulgarian and I live in Varna, if you have questions I may help you.
For schooling the children have options they to go to regular school or private school. The pre-school in Bulgaria starts when the kid is 5-6 years old and I am not sure that without it any school can take a kid. The other way is the kid to lose 1 school year. The children here go to school 1 grade 7 years old and really have to know Bulgarian.