It takes 3 or 3.5 hours by bus.
This bus service is available at Central Bus Station Sofia.
    ETAP ADRESS     BIOMET     Central Bus Station Sofia

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),
  Terminal 2 to Hotel Priska(XOTE* [Pi]**CKA): bus no. 284     Terminal 1 to Hotel Priska: bus no. 84
  Hotel Priska to Central Bus station (*EHTPA*HA [Gamma]APA): bus no. 213, (214), 305, 313.
Here we use * or [##] for Bulgarian letters.   If you can read Bulgarian letters, see transport map.
Usually it takes about 45 min. to 1 hour.
    Sofia Airport     transport map

There are also train service.   It takes about 4.5 hours
From Sofia, you have to change trains at GORNA ORJAHOVICA.
    Bulgarian railway company

It takes 3.5 or 4 hours by bus.
This bus service is available at Central Bus Station (avtogara)(only in Bulgarian) [bul Vladislav Varenchik 158]

Tourist Information center

Hotel	Phone	Fax	Distance for Build. 5	Prices
Interhotel Veliko Tarnovo	359-62-601000	359-62-639859	10 min. on foot	43/36 EUR (single lux/ord + breakfast)
Hotel Tarnovo	359-62-651199	----	10 min. on foot	20 EUR (single)
Hotel Etar	359-62-621838	359-062-621890	2 min. on foot	25 EUR/34 EUR (single/twin + breakfast)
Hotel Central	359-888-883906	----	10 min. on foot	50 EUR (single)
Best Western Hotel Premier	359-62-615555	359-62-603850	12 min. on foot	----