Bulgaria has four distinct seasons, and the best time depends entirely on what you're here for.
Spring (April–May) is the most pleasant time to travel the country broadly. Temperatures are mild (15–22°C), crowds are thin outside of Sofia, prices are at their lowest, and the countryside is green and flowering. The Rose Festival in the Valley of Roses near Kazanlak takes place in late May and early June — one of the more genuinely beautiful regional festivals in the Balkans.
Summer (June–August) brings peak heat (30–40°C in lowland areas) and peak crowds on the Black Sea coast. The coastal resorts get packed from late June through August, with prices rising accordingly. The mountains — Rila, Pirin, Rhodope — are ideal in summer, with good hiking conditions and refuges open. Sofia in August empties out as locals head for the sea or mountains.
Autumn (September–October) is arguably the best season overall. The coast has mostly cleared out by mid-September, but the sea is warm until October. Temperatures inland drop to comfortable levels (18–25°C). The forests in the mountains go gold and red. Wine country — the Thracian Valley around Plovdiv and Stara Zagora — is at its best during the grape harvest.
Winter (December–March) means skiing. Bulgaria's resorts — Bansko in the Pirin, Borovets in the Rila, and Pamporovo in the Rhodope — are significantly cheaper than the Alps. Bansko in particular has developed into a serious destination with modern lifts and a long season from December to April. Sofia in winter is cold and grey; the rest of the country largely shuts down for tourism, which can be peaceful or bleak depending on your disposition.