If you are thinking of going during the winter don't try going across from Varna and then down as you will have to go through the Stara Planina Mountains and that journey could be problematic in the winter. We did it in the summer driving across to Veliko Tarnavo and then down thro Gabravo and Abanassi. Its a nice journey but take supplies as it can be a bit remote. I wouldn't recommend unless you have a reliable car.
The main road through the middle of Bulgaria would be quicker.
I drove from Bansko to Bourgas four weeks ago. If I was coming from Varna I would either go via Sofia or Samakov. The road to Bansko via Velingrad from the Plovdiv highway is a very long scenic drive and is therefore further than it looks.