Bicing is not intended for \"long haul\" riding or heavy recreation. It's part of the city's public transport system and one of it's purposes is to ease congestion in the city center -- auto congestion and crowding on buses and metro lines.
So, it's really meant for short trips to take care of things in the center of the city. The maximum time you can use a bike is two hours. During the week I usually use it for 30 minutes or less at a time. Only on weekends do I take longer recreational rides, sometimes of up to two hours.
Regarding going to and from classes, it's not practical for me to use for most of my classes. But almost everyday I use it to get out of my neighborhood to a metro station, rather than walking or taking a bus to one. I also use it when I have a trip on two metro lines -- that is I substitute a bike ride for the first part of the journey and park the bike at the station I normally would be doing a transfer in. Ditto for getting home. So, I get a little exercise, I get to the metro (or home) a little faster and I get to spend a little more time outside.
Barcelona still does not have nearly enough bicycle lanes, but it has definitely improved over the years and I have heard there are plans to make more imrovements. We'll see about that.
As for Madrid being hilly and BCN being flat (Barcelona is NOT flat), well, I've lived in both cities and I don't think such a system (i.e. focused on the city center) would be unworkable in Madrid because of that. The traffic and drivers might be a challenege though. Which is where I guess bike lanes would come in.
Great to hear Sevilla's got a similar service. Yeah, the sweat can be a problem here, too, although I usually cool off on the metro before getting to class.
So, come on Madridlenos, get your bikes in gear!