There is a regular bus service from Madrid: Continental Auto; you can take the bus at Intercambiador Avenida América (Metro Avenida de América).
Hay un servicio regular de buses desde Madrid: Continental Auto; puedes tomar el bus en Intercambiador Avenida América (Metro Avenida de América).
Actually, I went from Santander to Burgos; the bus company is the same (Contiental Auto), so I took the bus in the morning in Santander, got off in Burgos at noon, spent the afternoon here and then went to Madrid.
En verdad, yo fui desde Santander hasta Burgos; la compañía de buses es la misma (Continental Auto), así que tomé el bus en la mañana en Santander, me bajé en Burgos al mediodía, pasé allí la tarde y luego seguí rumbo a Madrid.
For anyone coming to Spain and using the ferry, the bus down to Burgos is cheap and easy, going through the beautiful Cantabrian countryside. Price (October 2006) 10.12€ one way. Company is Continental Auto, times are:
Burgos to Santander
10.30, 16.00, 22.00 and 3.15
Santander to Burgos
8.00, 10.30, 16.30, 19.00, 0.30.
But check for holidays, weekends, and Fridays which all have slight variations.
Journey time is around three hours
I got the overnight train from Málaga to Burgos (normally only runs on Sundays). It was pretty cheap - 54.30€ including a litera in a shared compartment (women only). Down side, it was pretty cramped as there were six in the compartment and it was full. Two old Spanish dears got on in Cordoba and spent half the night talking or running in and out of the compartment for some bizarre reason. Times - 21.00 from Málaga, arrives Burgos 8.11 Monday morning but it was actually around an hour late.
The reason for doing this was to get the bus from Burgos to Santander to get the ferry to the UK. (The train actually goes on to Bilbao but the connections to Santander are appalling).
It was a good and relatively painless way to get to Burgos (and Santander - the onward bus trip was fine) if a little light on sleep. If anyone thinks about doing this, and wants a private compartment - book early. Some of the women I was travelling with had tried to get one but they were booked up. Similarly sometimes there are cheap offers on plane flights that work out as cheap as the train.
Anyone wanting to do it the other way round, the train leaves Burgos (from Bilbao) on a Friday night.
Ok, bit of an exaggeration but you can get a Gran Clase bus service between Santander and Madrid via Burgos.
Cost between Burgos and Madrid is around 22€ instead of the normal 15€ (approx). For which you get loads of space ie three seats across the bus not four. Endless (soft) drinks and/or tea and coffee, newspapers, and a ghastly snack.
I actually travelled Burgos to Madrid so at 8.15 they serve a Spanish breakfast if you choose, a prepackaged sweet cakey thing I think.
Oh and a film. Journey time is the same as the normal service ie 3 hours, but it was certainly very comfortable and saved waiting for the next (cheaper) bus an hour or two later.
If you use the train, it is easy enough to get to the town centre from the station - head straight down (towards the river) and turn right. Five or ten mins easy walk.
The bus station is on the right hand bank (facing north) ie same side as the railway station. When I went they were altering it, so all the buses left from the street - Calle de Madrid, northern ones on the north side of the street and southern direction ones on the other. It wasn't that easy to work out initially, although there are signs, sort of.
The bus station is still open for tickets, so you need to buy your ticket from the taquilla as usual. Find Calle Madrid and then turn down Calle Miranda (I think) for the ticket offices. My bus driver gave a Spanish guy a hard time for not having the proper ticket. Be warned!
The old town is on the left hand side of the river, and merits more time than I spent there. Lots of accommodation on that side too.
The railway station is quite close to the old city, on the other side of the river. You may walk there, but if you have lots of luggages, it´s better to take a cap.