Visit the RailEurope website to book travel for the Bucharest to Sofia (intercontinental) portion of your trip.
Select your preferred travel date, the number and type of tickets you would like and whether or not you prefer to travel economy or first class. Once you have done so, you will be shown a train trip that fits your specifications.
Book tickets and pay for them by credit card (Mastercard, Visa, Diner's Club or American Express). The tickets will then be mailed to you and will arrive within a few days.
Book travel from Sofia to Varna. To find a timetable, you will need to go to the Bulgarian State Railways website.
Use the drop-down list under 'Departure Station' and 'Destination Station' to select 'Sofia' and 'Varna' respectively. They are the first 2 names on the list, so you do not have to scroll all the way down to the alphabetical listings.
Make a note of your preferred train as Bulgarian State Railways do not allow you to order tickets online. You must reserve a ticket at the Sofia train station once you arrive.