You can get a bus but not from the airport, you have to go to bus terminal in sofia (not sure which one) about 10 - 20 leva taxi fare and 10 leva each way on the bus.
takes about three and a half hours and only stops in bladovgrad, razlog then bansko!!
Hi,
There is a link in the left hand column ( INFO AND SERVICES ) called TRANSPORT TO RESORTS..
Approx 70 Euro's ...let me know if you use it and its OK pls.
Cheers.