The classic and usually best value booking is to book the inbound and outbound on separate dates, say saturday to saturday, and then nest with a Sofia to Heathrow on the same dates, For a same day booking online I think you have a 2 hour minimum but the MCT at SOF is 60 so they can do it on the phone.

It's actually worth taking £30 off the UK to SOF flights with avios as you get 1p per avios (3000 avios) and about 6K back for the booking I think.