Yes, booklady, fondas could be the nearest concept to a bed & breakfast though they used to offer also lunch and dinner. I say "used to" because you won't find many nowadays in Madrid. In fact, I don't know any.
"Régimen de alojamiento y desayuno" is usually heard in hotels. They offer "alojamiento y desayuno" (bed & breakfast), "media pensión" (half-board) and "pensión completa" (full-board).
In Spain very few hostels give breakfast and, of course, don't expect them to be the yummy buffets you can find in some hotels.
By the way, it's curious to me that after living for 6 months in England 3 years ago, none of the 3 different families I lived with had an English breakfast.
The best tips from your favourite hostal in Madrid.
Hostal Chelo at http://www.chelo.com