If you're interested in skiing, then go in winter. Otherwise, it's best to go in summer or early autumn
Any season is good really. In the winter you can go skiing and snow fighting. in the spring, autumn and summer you can go hiking. The only time if the year the cable carts don't work is a few weeks in October, when they close for maintenance before the ski season starts. You can still go to the mountain by car, or public transportation.
The best time to be here is beginning of March- you get the best snow (Bansko) for skiing and not that cold. Summer is great for walking and playing golf. Many good places for food are working all year long but out of season you need to check where local people eats.
Get quick answers from Vitosha Mountain staff and past visitors.