Bilbao to Madrid

This may address your question in reverse, or may not answer it at all, but last November, we went from Madrid to Bilbao by train. It was an early train, and took all morning, but we arrived with time to visit the Guggenheim museum all afternoon. If I remember, the bus would've taken much longer (or maybe would've involved multiple buses), and while we flew from Bilbao to Barcelona later in the trip, we chose to not fly to Bilbao (either due to air schedules, getting to the Madrid airport, dealing with security and check-in times, cost, or a combination of these - don't exactly recall). For us, the train was the clear, best way to go north nine months ago, but not sure if that would work for you now, heading south.

The bus is faster by maybe forty-five minutes since the train has to swing way out toward Valladolid to stay on the tracks. They both cost about the same. Don't fly, both airports are way the hell and gone and getting up onto the mesa at Bilbao isn't always as easy as advertised.

Alsa has the bus scoop.

How ahead must one buy the tickets. Hopefully, I can purchase them the day before when I am sure of the traveling date.

The bus schedule has two Madrid destinations: Barajas Airport and Avda de America'

Our hotel is very near Plaza Mayor
Which would be better destination in order to get to our hotel? My gut is to go with the Airport since there are usually plenty of trains and other public transportation, but perhaps the Avda de America is on a close metro line?

Bad gut.

Five or six metro lines cross at Avenida de America. It's also umpteen million miles closer than the airport.

I agree with Ed, the airport isn't a short ride into town - go with Avenida de America.

For bus tickets, you need no advance purchase. I buy mine the afternoon/evening before simply for peace of mind and to plan my next day. Buses selling out is very rare and most bus riders buy their tickets last minute so the day before is never sold out. You don't need advance purchase to get a good fair like you do on the trains.

Thanks Brad. I don't care to buy tickets to early just in case there is a change of plans.

You folks are great! All of this advice and experience you so freely share is making me look like a real, experianced world traveler and all around global bon vivant.

Josh