There are plenty of low cost airlines flying to Varna. If you are driving, take the highway from Varna to Shumen. The distance is 87 km and it will take you approximately 1 hour to get to Shumen.
If you are not willing to drive, you may take a bus from Varna's central bus station. The airport is connected with the central bus station via bus line 409 which stops in front of the terminal. You may buy a ticket inside the bus (BGN 2 / EUR 1) or via the TicketVarna app (BGN 1 / EUR 0.50).
The price of the one-way ticket from Varna to Shumen is 10.45lv (EUR 5.50). The departure times are at 7am, 8.30am, 11am, 13.30pm, 18pm, 22.30pm. You may book your online ticket here: https://union-ivkoni.com/bg/
There are also some other local bus companies that run between Varna and Shumen but they only sell the tickets at the bus station itself. You may find the full timetable here: https://autogaravn.com/en
If you are feeling more adventurous, you may use the car sharing option with locals by searching for someone a few days in advance in this Facebook group: Пътуващи Варна <--> Шумен
All major airlines and low cost airlines fly to Sofia. If you are driving, take the road that goes through Veliko Tarnovo. If you have time, you can make a short stop there and have a sightseeing tour of our old capital. The full distance from Sofia to Shumen is 357km and it will take you approximately 4-5 hours to get there.
If you are not willing to drive, you may take a bus from Sofia's central bus station. The airport (Terminal 2) is connected with the central bus station via subway line M4 to Serdika station. There you will have to change to line M2 (Obelya) to Central Railway Station. The railway station is located right next to the central bus station. The journey will take approximately 40-50 minutes.
You may buy a ticket at the entrance of the metro station by tapping your card at the blue device (BGN 1.60 / EUR 0.80). The ticket is valid for 30 minutes and you will need to tap the same card at the entrance of each mode of transport (bus/metro/tram). You will not be charged extra within the 30 minutes. Only after that you will be charged extra BGN 1.60 with the daily limit being capped at BGN 4 (EUR 2) acting as a "Day card".
The price of the one-way ticket from Sofia to Shumen is 30lv (EUR 15). The departure times are at 6am, 9.30am, 11am, 12.30pm, 15.30pm, 17pm, 19.30pm, 22.30pm. You may book your online ticket here: https://union-ivkoni.com/bg/
If you are feeling more adventurous, you may use car sharing with locals by searching for someone a few days in advance in this Facebook group: Пътуващи Варна <--> Шумен
All major airlines and low cost airlines fly to Bucharest. If you are driving, take the road that goes through Ruse. The full distance from Bucharest to Shumen is 220km and it will take you approximately 3 hours to get there.
IMPORTANT: the Danube Bridge crossing between Romania (Giurgiu) and Bulgaria (Ruse) is undergoing massive reconstruction. Therefore, there is a lot of traffic, lines and delays. Last time we crossed the bridge it took us 2 hrs to get from Giurgiu to Ruse. So make sure you plan accordingly.
If you are not willing to drive, you may take a bus from Bucharest via obilet.com, flixbus.bg or pegasusbg.com/
The price of the one-way ticket from Bucharest to Shumen is EUR 22. The departure times are at 4.15am or 14.30pm with Pegasus (departing from Hotelul Horoscop) or at 22:45pm with FlixBus.