If you use airplan, you would arrive at either Sofia AIrport or Varna Airport.

Local bus services are abailable. But there are no services which take you directly to the cenrtaral bus station.
If you know "Hotel Priska" (it is also the name of bus stop),
  Sofia Airport to Hotel Pliska(XOTE* {Pi]**CKA): bus no. 84
        about 25 minutes (Hotel Priska is the 16th stop from Terminal 2),     comes every 14 minutes on holidays
  Hotel Priska to Central Bus station (*EHTPA*HA ABTO[Gamma]APA): bus no. 213, 214, 305, 413
        about 25 minutes,     each line, comes every 20 minutes.
Here we use * or [##] for Bulgarian letters.
If you can read Bulgarian letters, see transport map.
    Sofia Airport     transport map (local bus service)     Central Bus Station Sofia         tram service

It takes 3 or 3.5 hours by bus.
This bus service is available at Central Bus Station Sofia.
    ETAP ADRESS / Group plus (only in Bulgarian)     BIOMET     UNION IVOKONI (only in Bulgarian)

Tickts are     21 Lvs (one way)       35 Lvs (round trip)     from Sofia to Veliko Tarnovo.

There are also train service.   It takes about 4.5 hours
The Sofia station is near the Central Bus Station Sofia
From Sofia, you have to change trains at GORNA ORJAHOVICA.
    Bulgarian State Railway     Bulgarian Railway map     Information

It takes 3.5 or 4 hours by bus.
This bus service is available at Central Bus Station (avtogara) (only in Bulgarian)
    Varna Airport