If your bus is from ALSA company you have three different bus stations from Barna and only one in Madrid.

For Madrid is Avda de América which is not right at the center but can be consider near the center (is inside the M30 ring) and very well communicated with 4 metro lines and buses to many other places of spain and nearby towns of Madrid.

As you can see there aren't central bus stations in Madrid and Barna, for Madrid there is also Estación Sur de Autobuses and some other company-owned stations such as La Sepulvedana in Principe Pio and Auto-Res in Conde de Casal.