I did my B2B to Sofia yesterday, many other people were doing the same or staying for a night! It was easy for sure but I would definitely recommend getting your Sofia-London boarding pass before your London-Sofia one.
Just to flag, I don't have a UK/EU passport and while checking in for my Sofia-London flight, I was flagged on the system because I needed to show passport and visa documentation for the flight (even though I don't need a visa). I got off the flight and closer to boarding time, I went to the gate to find a BA representative. They scanned my BP and the red light popped up "Boarding denied", but I showed them my passport, they did a few things behind the computer, and all went well thankfully.
Doing another run to Sofia next weekend but with a one night stay, maybe I'll see others doing the same.