We travelled around Bulgaria by buses and trains and didn't have any bad experiences with either of them.
By bus
Bulgarian roads are not in the best state. Most of them are narrow, real highways still need to be built. Bulgarian drivers however are relaxed, adjusting their way of driving to the road conditions most of the times, which makes for relatively pleasant bus journeys.
Bus network is dense, connections between major centres frequent and buses on most frequented routes in good condition. Buses meandering narrow roads to smaller villages are naturally smaller and they tend to be older. Several villages, for example Melnik, only have one bus connection per day.
We always bought bus tickets in advance, at the bus stations. Buying a bus ticket in Sofia might be a little bit tricky, as the new bus terminal is filled with dozens of small ticket booths, each of them belonging to a different private company servicing different routes. If you are unable to spot your destination, ask the information counter which company sells tickets for the place you want to go to. When we asked the staffs at the information counter were friendly, very helpful and they spoke English.
When planning our trip around Bulgaria we used Sofia Central Bus Terminal website a lot as it has very useful information on all the bus schedules.
By train
Despite Bulgarian trains are old and slow, travelling by train is somehow more comfortable than by bus, as you can always walk around and stretch your legs.
Majority of trains we took had minor delays of less than half an hour which haven't caused any incoveniences.
More information on rail connections and train schedules in Bulgaria is available at Bulgarian railways website.