Hi, bluemoon,
Welcome to the forum. Hope we can help with your travel question.
My opinion would be that it´s much easier to fly in and out of Madrid. If you go on to Bilbao, you´re likely to have to change in the Madrid airport anyway (or else fly through London and then go London to Bilbao, but that might involve a change in airports in London).
There´s no doubt that pickpockets abound in Madrid, but the way to remove all worries is to put your valuables in a pocket under your shirt. It´s easy to have passport, credit cards, cash, etc. all out of reach, so then you don´t even have to worry about being alert.
You don´t say whether you plan to go by bus or train to Astorga, but either way, the public transportation options from the airport are great. You can decrease the pickpocket factor enormously by staying off the metro. That would mean taking either a bus (there´s a bus from the airport that goes directly to the Av. Américas bus station) or a commuter train (there´s a direct Cercanías train that goes from the airport to the Chamartín train station). I can find more information on either of these options if it would help you. Buen camino, Laurie