The two low cost carriers who fly to Sofia in Bulgaria are Wizz Air and Easyjet

Wizz Air flies from Luton to Sofia. There are usually five flights per week and cost is usually £50 - £70 each way. If you book early sometimes flights can be had for as little as £25 each way.

Easyjet flies from Gatwick to Sofia every day. Cost is similar to Wizz Air. Again, it is best to book early.

It is possible to fly to Plovdiv which is closer to Bansko. These tend to be charter flights. Try http://www.charterflights.co.uk/.

British Airways flies from Heathrow to Sofia daily. Bulgarian Air flies from Manchester, Gatwick and Heathrow to Sofia. These tend to be a bit more expensive than the low cost cariers but they do have special offers ocassionally.

There are several companies that provide taxi and minibus services from the airports to Bansko. It is important to pre-book these.  Try Property Management BG or search for "sofia bansko taxi" on google. Prices start from around 85 Euro each way for a car taxi.

A new company called banskoexpress.com has started this season. Prices are very low (2 persons £18, 4+ persons £12 each way per person). This is sharing a car or bus depending upon numbers.  I am going to give this a go this season and see how they work out.

All the major car hire companies have agencies at the airports if you want to drive.