Varna.info : Travel to Varna :

Sofia to Varna

There are different modes of transport to choose from for your travel from Sofia to Varna. The distance between these two cities is 470km. You can travel by air if you need to get there fast. But if time is not a constraint and you want to take a leisurely trip, you can choose between traveling by train and bus.

Flight to Varna
This is by far the quickest and easiest mode of transport. The flight takes just about an hour. You can book your flight up to fourteen days in advance. The cost of a one-way ticket is around 90 lev, which is under 50 Euros. The flights are carried out every Friday and Sunday from 7am.
http://wizzair.com/

By Train
It takes around 7 to 8 hours to get to Varna from Sofia by train. A one-way ticket in an express train would cost just around 25 lev. Train travel is extremely inexpensive in Bulgaria. However prices vary according to the speed of the train service as well as the day of the week it is operated on. Tourists may catch the train from Sofia to Varna at 9.05 am /through Plovdiv/, 10.15 am, 12.35 pm, 10.25 pm. The express train departs for Varna in 7.45 am.
http://bdz.creato.biz/en

By Bus
Some people prefer to travel to Varna by bus. The price for a ticket is almost the same as the fare by train. Buses which do not make many stops manage to safe an hour of travel time when compared to trains. There are also luxury bus services that are more comfortable to travel by. Different bus companies have different schedule for departure to Varna. Busses of Group Company depart from Sofia to Varna at 7.30am, 8 am, 2.30 pm and 6pm; Etap-Adress Company – 11am, 12.30pm, 1.30pm, 3pm, 4pm, 7pm and 10.30pm; while the schedule to Varna of one of the most popular Bulgarian bus companies Biomet is 7.30am, 1pm, 4pm, 10.30pm.
http://www.centralnaavtogara.bg/

Traveling by buses and trains is one of the best ways to see the countryside and meet many local people and tourists as well. This mode of travel is the cheapest and trains especially are quite punctual.

By Car
You can reach Varna from Sofia using European route E70 (Varna-Shumen), European route E772 (Shumen-Yablanitsa) and European route E83 (Yablanitsa-Sofia). The Haemus motorway (A2), which is under construction, is a direct motorway between Sofia and Varna.