I have just called. There is a locker service where you can leave your luggage up to 45 days. It is located at the docks level, just in front of dock #60.

BTW, I don't know if the use of the word 'dock' is correct in this context in English or not. In some Spanish Bus stations, like this one, use the same word used in harbours 'dársena' (dock). In some others, they use the same word as in train stations 'andén' (platform).

In Madrid, the Bus Station (Mendez Alvaro) does not use lockers for their baggage storage. They use shelves.

Actual storage lockers can be found at Chamartin and Atocha Train stations.

The Airport has both Lockers and shelves depending on which one of their storage centers you go to.

The best thing to do is see where you are traveling to and from and then counting the number of days you need to store something in order to see where you should store it.