Mountain Rescue services are paid in Bulgaria and the best way to cover such an expenses is to have a valid insurance. It can be your International Travel Insurance that covers medical costs and mountain rescue during activities like hiking up to 3000 m. elevation (check that) or obtained in Bulgaria mountain insurance. But keep in mind that the standard one that you can buy from the tourist offices here has restrictions on the type of accidents that are covered and also refunds expenses up to 1000 leva (approximately 500 EUR) which may not be sufficient if covering a helicopter assistance or multiday researches. If you prefer to have a better coverage (including helly-rescue), ask for a higher limit of the rescue expenses on your local insurance.
Bulgarian Mountain Rescue (PSS, ПСС) has bases with 24/7 staff in the most popular mountain areas. In case of emergency you can contact them via +359 14 70 or 112.