Flying from the UK, I have checked and double checked flights into Madrid v Bilbao against trains and buses, and until I reach Carrion de los Condes, Bilbao always comes out on top.
Admittedly, Bilbao suits me best to fly to and from as I get the best deal using my Avios/airmiles as it's only 8,000 per return trip. The aerobus into the central bus station runs every 20-30 minutes and takes around 25 minutes. It's a very small airport so it's all very easy to negotiate and find your way around.
My next stage of the Camino I will be walking Navarrete to (probably) Carrion de los Condes - and as long as I get the 17-something pm bus back to Burgos for the night, I shall stay there, explore and get an early afternoon bus (less than 2 hours) back to Bilbao in time for my early evening flight back to Heathrow.
My research shows me travel to Carrion de los Condes and before is best via Bilbao, but to Sahagun and after, then Madrid comes out best.