Shuttle T1T2T3 to T4 is 8 minutes. I can't find frequency of service. If it is one shuttle doing the rounds you could end up waiting as much as half an hour if you just miss it.
While 55 minutes is definately very tight to make your bus, 2 hours and 45 minutes is lots of time to get from airport to Chamartin.
T1T2T3 to train station Chamartin is best achieved with Madrid Metro. It runs frequently. I'd allow an hour.
Renfe website with my limited understanding of Spanish indicates you can buy a ticket while on the train but that is a cash only purchase. You can buy tickets at the station just prior to boarding. There have been reports of long line ups while ticket machines go unused. The ticket machines are apparently Spanish only. For your timings ... I'd suggest purchase in advance.
If you use train as plan B ... If you get to T4 and miss your bus you can buy your Renfe ticket to Leon at the Renfe Cercanius desk. Cercanius is fastest way to Chamartin but runs only every half hour.
2002
Madrid Airport
The airport in Madrid is called Adolfo Suárez Madrid-Barajas Airport (MAD). There are 4 terminals. T1, T2, and T3 are connected while T4 is connected via shuttle. Terminal 4S is connected to Terminal 4 by Automatic People Mover (APM) and has a shuttle stop.
Madrid Airport (MAD)
http://www.aena-aeropuertos.es/csee/Satellite/Aeropuerto-Madrid-Barajas/en/
Information about the shuttle to T4 is located here
http://www.aena-aeropuertos.es/csee...554331229//Connections-between-terminals.html
2003
Getting around in Madrid
Connections to Madrid include subway (Metro), light rail transit (Cercanius), and Express bus (EMT).
Madrid Metro has stations at T1-T2-T3 and at T4. The trains run every 6 - 12 minutes.
Madrid Cercanius has a station at T4. The trains run every 30 minutes.
EMT Madrid Aeropuerto Express operates a bright yellow express bus every 13 -20 minutes from the airport T1-T2-T3 and airport T4 to Puerta de Atocha Renfe station.
Madrid Metro
http://www.metromadrid.es/en/index.html
Madrid Metro Map
http://www.metromadrid.es/export/sites/metro/comun/documentos/planos/Planomayo2013.pdf
Madrid Cercanius (operated by Renfe)
http://www.renfe.com/viajeros/cercanias/madrid/index.html
EMT Madrid provides Madrid transit bus services
http://www.emtmadrid.es/
EMT Madrid Aeropuerto Express
http://www.emtmadrid.es/lineaAeropuerto/index.html
2004
Train Service Madrid
Renfe operates Spain's national train network.
Renfe
http://www.renfe.com/index.html
2007
Madrid Airport to train station Chamartin
a. Chamartin is reached by Metro. Take line 8 from airport T1-T2-T3 or T4 to Nuevos Ministerios; and, line 10 to Chamartin.
b. Chamartin is reached by Renfe Cercanius direct from Madrid Airport T4.