So here is my experience, to help others who might read this:
- Bus A2 from/to airport is a proper coach bus, not a city bus. Luggage storage underneath but you have to open the door, drivers do not do it. Very comfortable, one hour from airport to Sofitel on Corniche Rd.
- Fare is 4 dirhams, all journey within the city are 2 dirhams. You use a Halifat card, can be bought (10 dirhams for the card plus 30 dirhams charged on it) at machines (at the airport stop, selected stop in the city and Lulu supermarket in town)
- Plenty of routes, I never had too much of a problem going anywhere (Louvre, Grand Mosque, Marina, Old Fort)
- Drivers drive well and safely, more than taxis
- Several stops have a clever display: it looks like paper but is actually electronic and shows in real time the next buses
- The next stop might or might not be displayed inside the bus, so better be on the look out.

Overall a surprisingly good experience.