Since 1st January 2014 EU or EEA citizens can buy property in Bulgaria without restrictions.
Non-EU or EEA citizens cannot buy properties in Bulgaria that includes land, for example a house in a plot of land, or an apartment with ideal parts of the land the block was built on, but they have the possibility to buy property without restrictions as long as the property is bought by means of a Bulgarian company.
The first step for a Non-EU or EEA citizen to buying a property in Bulgaria thus is to register a Bulgarian company.
You can obtain additional information at:
https://www.gov.uk/how-to-buy-property-in-bulgaria
http://www.property-in-bulgaria.bg/