I am planning a segment of a trip for October. (Our first retirement trip, so time is flexible.) As of now, I have us leaving Istanbul, flying into Varna. After spending about a week on the coast, we will head to Plovdiv for 5-7 days and Sophia for 5-7 days. My question is about time spent on the coast. Is it best to have one base (Varna? Nessebar? Burgas?) or would it be best to split the time between locations? (Move south as we get ready to head to Plovdiv?) We won't have a car, but rely on public transit. Are there good options for public transit along the coast if we decide to have one base and then take day trips? I am going to look into hired transport to move us to Plovdiv and then Sophia, and perhaps this is the best option for the coast, as well? Any suggestions will be appreciated.
In 2015 I was able to get from Burgas to Nesebar and Sozopol (on separate days) by public bus. I can't tell you anything about bus frequency, though.
I'd recommend doing some careful research before choosing your coastal base(s). I believe there are rather a lot of tacky, low-end beach resorts in that area. The area was a popular destination for cheap sunshine before the Berlin Wall came down, and I have the feeling (yeah, this is not based on personal observation) the situation may not have changed much.
I was able to reach Sofia, Plovdiv and Veliko Tarnovo (also worthwhile) by public transportation. Trains, however, were very slow--not faster than buses; figure on about 30 mph. Your willingness to pay for private transportation, if necessary, may come in handy. It's nice to have that as an option if the public-transportation schedules do not align with your preferred itinerary. But you may be able to manage without it if you're patient travelers.
The towns of Burgas and Varna are iteresting but for me the most interesting and enjoyable was Nessebar. When I was there before the war there were a lot of russians and I would presume that is no longer the case so it might be even nicer now. The tacky end was Sunny Beach, not a lot of redeming value there. But Nessebar keeps calling me back. That and Provdiv. As much as I enjoyed Sofia I cant imagine staying busy for 7 days ... Veliko Tarnovo was another nice stop. And if you can find transportation look for Devil's Throat. Its interesting and getting there is one of those Death Road Trucker movies. You'll never forget it. Bulgaria is full of wonderful little villages and towns. Do the research or ask a guide, they are worth the stops. Love it there.
EDIT: The Septemvri–Dobrinishte narrow-gauge line. If you can link two stops with that its worth every second of the ride. I rode it from Avramovo to Bansko (yes, I did have to look that up).
EDIT, EDIT: and Asen's Fortress and Bachkovo Monastery and the Rila Monastery of course.