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.
Get quick answers from Vitosha Mountain staff and past visitors.