I am not a fan of bus travel, so I try to fly or take a train at the start and end of the camino.
But here are the other things that you might want to weigh.
--Which is closest to where you arrive in Madrid? From the airport terminal T4, you can get right on a bus, so that means you don't have to even go into Madrid. But of course you may want to go into Madrid to spend a day or two in that lovely city.
-- Look at the schedules and figure out which works best for your arrival time.
--Bus costs a lot less than train usually, unless you get a cheap online fare or unless you're over 60 and can buy a tarjeta dorada and get a good discount.
Taking the train is really a piece of cake, especially if you arrive in T4 (which you will if you are flying Iberia or one of its code share partners, namely American and BA). You can take the Cercanias commuter train to the Atocha train station, which is quick and easy.
Buen camino, Laurie