A good place to park / lock / store a bicycle in Madrid for a month?

I am going back from Madrid to my home town, then returning to Madrid after a month to fly to South America from there. I have my bicycle which I want to take with me to South America - but won't need my bike in cold winter weather of Estonia in the meantime and flying there and back with the bike with connecting flights is extremely expensive and a very big hassle.

Luggage storage services for a month for such a big item would probably also cost earth, and I don't know anyone in Madrid, so I need to find out if there's a (relatively) safe place to lock and keep my bicycle for that time? Maybe there are some large covered bicycle parking lots where the bike could be parked for a bit longer stay?