I should imagine that any albergue in Santiago would allow you to leave your bike for pick up as long as you asked them in advance. During my more recent caminos I have found the albergue floor at the Hospedario San Martin Pinario to be a VERY good stop in Santiago!
Most pilgrim rooms are singles at 23 Euros. Ask about these when you email your query. for space to this address >>
reservas@sanmartinpinario.eu. Do NOT use their on-line booking form which is only for more expensive and more elegant regular tourist accommodation.
I stayed in their simple pilgrim rooms in December 2011, 2012, and 2013 and found them comfortable and the location most convenient. They are open 24/7 so that you can arrive at anytime, the obliging desk staff are multi-lingual, WiFi is free, there are multiple public spaces for casual conversation and the restaurant (open to all) serves a very good 3 course lunch or dinner with wine for only 12 Euros. What more does a tired pilgrim need?
Buen Camino,
Margaret Meredith